How to find the area of a triangle - ISEE Lower Level Quantitative Reasoning

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Question

A right triangle has a base of 4 and a height of 7.

What is the triangle's area?

Answer

An area of a triangle is

$\frac{1}{2}\times base\times height$

In this case

$\frac{1}{2}\times 4\times 7=14$

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Question

What is the area of a triangle with a base of 7cm and a height of 4cm?

Answer

Use the formula for the area of a triangle

$\frac{1}{2}bh$

to solve this problem. Plug in and you get $14\ cm^{2}$ .

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Question

What is the area of a triangle with a base of 8 and a height of 3?

Answer

The area of a triangle is $\frac{1}{2}(base height)$ . We know that our base is 8 and our height is 3.

In this case, the equation is $\frac{1}{2}(8 3)$ . Now we can solve this equation.

$\frac{1}{2}(24)$

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Question

What is the area of a triangle that has a base of 7 and a height of 10?

Answer

To find the area of a triangle, we use $\frac{1}{2}(base height)$ . We know the height of the triangle is 10 and the base is 7.

$\frac{1}{2}(baseheight)=\frac{1}{2}(710)$

$\frac{1}{2}*(70)$

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Question

The height of a triangle is ft. The base is ft. What is the area of the triangle?

Answer

The formula for finding the area of a triangle is $\frac{1}{2}(base\times height)$ . Multiply the base times the height first. $8\times6=48$ . Then, either multiply $\frac{1}{2}\times\frac{48}{1}$ , or simply divide $48\div2$ . Therefore the answer is $24ft^{2}$ .

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Question

If the base of a triangle is 12 cm, and the height of the triangle is 4 cm, what is the total area of the triangle?

Answer

First, you must remember the formula for the area of a triangle $(A=\frac{1}{2}bh)$ .

Plug in the given values: $A=\frac{1}{2}(4)(12)$ .

Multiply to get 24. Since this is area, the units must be sqaured. Therefore, your final answer is $24\ cm^2$ .

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Question

What is the area of the right triangle in the following figure?

Answer

There are several different ways to solve for the area of a right triangle. In this lesson, we will transform the right triangle into a rectangle, use the the simpler formula for area of a rectangle to solve for the new figure's area, and divide this area in half in order to solve for the area of the original figure.

First, let's transform the triangle into a rectangle:

Second, let's remember that the formula for area of a rectangle is as follows:

$A=l\times w$

Substitute in our side lengths.

$A=13\times 9$

Last, notice that our triangle is exactly half the size of the rectangle that we made. This means that in order to solve for the area of the triangle we will need to take half of the area of the rectangle, or divide it by .

$117\div 2= 58.5\textup{ in}^2$

Thus, the area formula for a right triangle is as follows:

$A=\frac{1}{2}(l\times w)$ or $A=\frac{l\times w}{2}$

Compare your answer with the correct one above

Question

What is the area of the right triangle in the following figure?

Answer

There are several different ways to solve for the area of a right triangle. In this lesson, we will transform the right triangle into a rectangle, use the the simpler formula for area of a rectangle to solve for the new figure's area, and divide this area in half in order to solve for the area of the original figure.

First, let's transform the triangle into a rectangle:

Second, let's remember that the formula for area of a rectangle is as follows:

$A=l\times w$

Substitute in our side lengths.

$A=12\times 8$

Last, notice that our triangle is exactly half the size of the rectangle that we made. This means that in order to solve for the area of the triangle we will need to take half of the area of the rectangle, or divide it by .

$96\div 2= 48\textup{ in}^2$

Thus, the area formula for a right triangle is as follows:

$A=\frac{1}{2}(l\times w)$ or $A=\frac{l\times w}{2}$

Compare your answer with the correct one above

Question

What is the area of the right triangle in the following figure?

Answer

There are several different ways to solve for the area of a right triangle. In this lesson, we will transform the right triangle into a rectangle, use the the simpler formula for area of a rectangle to solve for the new figure's area, and divide this area in half in order to solve for the area of the original figure.

First, let's transform the triangle into a rectangle:

Second, let's remember that the formula for area of a rectangle is as follows:

$A=l\times w$

Substitute in our side lengths.

$A=11\times 9$

Last, notice that our triangle is exactly half the size of the rectangle that we made. This means that in order to solve for the area of the triangle we will need to take half of the area of the rectangle, or divide it by .

$99\div 2= 49.5\textup{ in}^2$

Thus, the area formula for a right triangle is as follows:

$A=\frac{1}{2}(l\times w)$ or $A=\frac{l\times w}{2}$

Compare your answer with the correct one above

Question

What is the area of the right triangle in the following figure?

Answer

There are several different ways to solve for the area of a right triangle. In this lesson, we will transform the right triangle into a rectangle, use the the simpler formula for area of a rectangle to solve for the new figure's area, and divide this area in half in order to solve for the area of the original figure.

First, let's transform the triangle into a rectangle:

Second, let's remember that the formula for area of a rectangle is as follows:

$A=l\times w$

Substitute in our side lengths.

$A=10\times 7$

Last, notice that our triangle is exactly half the size of the rectangle that we made. This means that in order to solve for the area of the triangle we will need to take half of the area of the rectangle, or divide it by .

$70\div 2= 35\textup{ in}^2$

Thus, the area formula for a right triangle is as follows:

$A=\frac{1}{2}(l\times w)$ or $A=\frac{l\times w}{2}$

Compare your answer with the correct one above

Question

What is the area of the right triangle in the following figure?

Answer

There are several different ways to solve for the area of a right triangle. In this lesson, we will transform the right triangle into a rectangle, use the the simpler formula for area of a rectangle to solve for the new figure's area, and divide this area in half in order to solve for the area of the original figure.

First, let's transform the triangle into a rectangle:

Second, let's remember that the formula for area of a rectangle is as follows:

$A=l\times w$

Substitute in our side lengths.

$A=9\times 6$

Last, notice that our triangle is exactly half the size of the rectangle that we made. This means that in order to solve for the area of the triangle we will need to take half of the area of the rectangle, or divide it by .

$54\div 2= 27\textup{ in}^2$

Thus, the area formula for a right triangle is as follows:

$A=\frac{1}{2}(l\times w)$ or $A=\frac{l\times w}{2}$

Compare your answer with the correct one above

Question

What is the area of the right triangle in the following figure?

Answer

There are several different ways to solve for the area of a right triangle. In this lesson, we will transform the right triangle into a rectangle, use the the simpler formula for area of a rectangle to solve for the new figure's area, and divide this area in half in order to solve for the area of the original figure.

First, let's transform the triangle into a rectangle:

Second, let's remember that the formula for area of a rectangle is as follows:

$A=l\times w$

Substitute in our side lengths.

$A=8\times 5$

Last, notice that our triangle is exactly half the size of the rectangle that we made. This means that in order to solve for the area of the triangle we will need to take half of the area of the rectangle, or divide it by .

$40\div 2= 20\textup{ in}^2$

Thus, the area formula for a right triangle is as follows:

$A=\frac{1}{2}(l\times w)$ or $A=\frac{l\times w}{2}$

Compare your answer with the correct one above

Question

What is the area of the right triangle in the following figure?

Answer

There are several different ways to solve for the area of a right triangle. In this lesson, we will transform the right triangle into a rectangle, use the the simpler formula for area of a rectangle to solve for the new figure's area, and divide this area in half in order to solve for the area of the original figure.

First, let's transform the triangle into a rectangle:

Second, let's remember that the formula for area of a rectangle is as follows:

$A=l\times w$

Substitute in our side lengths.

$A=7\times 4$

Last, notice that our triangle is exactly half the size of the rectangle that we made. This means that in order to solve for the area of the triangle we will need to take half of the area of the rectangle, or divide it by .

$28\div 2= 14\textup{ in}^2$

Thus, the area formula for a right triangle is as follows:

$A=\frac{1}{2}(l\times w)$ or $A=\frac{l\times w}{2}$

Compare your answer with the correct one above

Question

What is the area of the right triangle in the following figure?

Answer

There are several different ways to solve for the area of a right triangle. In this lesson, we will transform the right triangle into a rectangle, use the the simpler formula for area of a rectangle to solve for the new figure's area, and divide this area in half in order to solve for the area of the original figure.

First, let's transform the triangle into a rectangle:

Second, let's remember that the formula for area of a rectangle is as follows:

$A=l\times w$

Substitute in our side lengths.

$A=14\times 10$

Last, notice that our triangle is exactly half the size of the rectangle that we made. This means that in order to solve for the area of the triangle we will need to take half of the area of the rectangle, or divide it by .

$140\div 2= 70\textup{ in}^2$

Thus, the area formula for a right triangle is as follows:

$A=\frac{1}{2}(l\times w)$ or $A=\frac{l\times w}{2}$

Compare your answer with the correct one above

Question

What is the area of the right triangle in the following figure?

Answer

There are several different ways to solve for the area of a right triangle. In this lesson, we will transform the right triangle into a rectangle, use the the simpler formula for area of a rectangle to solve for the new figure's area, and divide this area in half in order to solve for the area of the original figure.

First, let's transform the triangle into a rectangle:

Second, let's remember that the formula for area of a rectangle is as follows:

$A=l\times w$

Substitute in our side lengths.

$A=15\times 11$

Last, notice that our triangle is exactly half the size of the rectangle that we made. This means that in order to solve for the area of the triangle we will need to take half of the area of the rectangle, or divide it by .

$165\div 2= 82.5\textup{ in}^2$

Thus, the area formula for a right triangle is as follows:

$A=\frac{1}{2}(l\times w)$ or $A=\frac{l\times w}{2}$

Compare your answer with the correct one above

Question

What is the area of the right triangle in the following figure?

Answer

There are several different ways to solve for the area of a right triangle. In this lesson, we will transform the right triangle into a rectangle, use the the simpler formula for area of a rectangle to solve for the new figure's area, and divide this area in half in order to solve for the area of the original figure.

First, let's transform the triangle into a rectangle:

Second, let's remember that the formula for area of a rectangle is as follows:

$A=l\times w$

Substitute in our side lengths.

$A=16\times 12$

Last, notice that our triangle is exactly half the size of the rectangle that we made. This means that in order to solve for the area of the triangle we will need to take half of the area of the rectangle, or divide it by .

$192\div 2= 96\textup{ in}^2$

Thus, the area formula for a right triangle is as follows:

$A=\frac{1}{2}(l\times w)$ or $A=\frac{l\times w}{2}$

Compare your answer with the correct one above

Question

What is the area of the right triangle in the following figure?

Answer

There are several different ways to solve for the area of a right triangle. In this lesson, we will transform the right triangle into a rectangle, use the the simpler formula for area of a rectangle to solve for the new figure's area, and divide this area in half in order to solve for the area of the original figure.

First, let's transform the triangle into a rectangle:

Second, let's remember that the formula for area of a rectangle is as follows:

$A=l\times w$

Substitute in our side lengths.

$A=17\times 13$

Last, notice that our triangle is exactly half the size of the rectangle that we made. This means that in order to solve for the area of the triangle we will need to take half of the area of the rectangle, or divide it by .

$221\div 2= 110.5\textup{ in}^2$

Thus, the area formula for a right triangle is as follows:

$A=\frac{1}{2}(l\times w)$ or $A=\frac{l\times w}{2}$

Compare your answer with the correct one above

Question

What is the area of the right triangle in the following figure?

Answer

There are several different ways to solve for the area of a right triangle. In this lesson, we will transform the right triangle into a rectangle, use the the simpler formula for area of a rectangle to solve for the new figure's area, and divide this area in half in order to solve for the area of the original figure.

First, let's transform the triangle into a rectangle:

Second, let's remember that the formula for area of a rectangle is as follows:

$A=l\times w$

Substitute in our side lengths.

$A=18\times 14$

Last, notice that our triangle is exactly half the size of the rectangle that we made. This means that in order to solve for the area of the triangle we will need to take half of the area of the rectangle, or divide it by .

$252\div 2= 126\textup{ in}^2$

Thus, the area formula for a right triangle is as follows:

$A=\frac{1}{2}(l\times w)$ or $A=\frac{l\times w}{2}$

Compare your answer with the correct one above

Question

What is the area of the right triangle in the following figure?

Answer

There are several different ways to solve for the area of a right triangle. In this lesson, we will transform the right triangle into a rectangle, use the the simpler formula for area of a rectangle to solve for the new figure's area, and divide this area in half in order to solve for the area of the original figure.

First, let's transform the triangle into a rectangle:

Second, let's remember that the formula for area of a rectangle is as follows:

$A=l\times w$

Substitute in our side lengths.

$A=13\times 8$

Last, notice that our triangle is exactly half the size of the rectangle that we made. This means that in order to solve for the area of the triangle we will need to take half of the area of the rectangle, or divide it by .

$104\div 2= 52\textup{ in}^2$

Thus, the area formula for a right triangle is as follows:

$A=\frac{1}{2}(l\times w)$ or $A=\frac{l\times w}{2}$

Compare your answer with the correct one above

Question

What is the area of the right triangle in the following figure?

Answer

There are several different ways to solve for the area of a right triangle. In this lesson, we will transform the right triangle into a rectangle, use the the simpler formula for area of a rectangle to solve for the new figure's area, and divide this area in half in order to solve for the area of the original figure.

First, let's transform the triangle into a rectangle:

Second, let's remember that the formula for area of a rectangle is as follows:

$A=l\times w$

Substitute in our side lengths.

$A=13\times 7$

Last, notice that our triangle is exactly half the size of the rectangle that we made. This means that in order to solve for the area of the triangle we will need to take half of the area of the rectangle, or divide it by .

$91\div 2= 45.5\textup{ in}^2$

Thus, the area formula for a right triangle is as follows:

$A=\frac{1}{2}(l\times w)$ or $A=\frac{l\times w}{2}$

Compare your answer with the correct one above

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