Pre-Algebra : Area

Study concepts, example questions & explanations for Pre-Algebra

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Example Questions

Example Question #31 : Area Of A Triangle

Find the area of a triangle with a base of 4cm and a height that is two times the base.

Possible Answers:

\(\displaystyle 16\text{cm}\)

\(\displaystyle 4\text{cm}^2\)

\(\displaystyle 16\text{cm}^2\)

\(\displaystyle 32\text{cm}^2\)

\(\displaystyle 32\text{cm}\)

Correct answer:

\(\displaystyle 16\text{cm}^2\)

Explanation:

The formula to find the area of a triangle is

\(\displaystyle A = \frac{1}{2} \cdot b \cdot h\)

where is the base and h is the height.  We know the base of our triangle is 4cm.  We know the height is two times the base, so the height is 8cm.  Now, we substitute

\(\displaystyle A = \frac{1}{2} \cdot 4\text{cm} \cdot 8\text{cm}\)

\(\displaystyle A = 2\text{cm} \cdot 8\text{cm}\)

\(\displaystyle A = 16\text{cm}^2\)

Therefore, the area of the triangle is \(\displaystyle 16\text{cm}^2\).

Example Question #33 : Area Of A Triangle

The base of a triangle is \(\displaystyle 4\) inches, and the height of the triangle is \(\displaystyle 9\) inches.  What is the area of the triangle?

 

Possible Answers:

\(\displaystyle 16\) square inches

\(\displaystyle 17\) square inches

\(\displaystyle 18\) square inches

\(\displaystyle 19\) square inches

\(\displaystyle 15\) square inches

Correct answer:

\(\displaystyle 18\) square inches

Explanation:

To find the area of a triangle, multiply the base by the height, and divide by two.  The best answer is:

\(\displaystyle 18\) square inches

Example Question #34 : Area Of A Triangle

The base of a triangle is \(\displaystyle 12\) inches, and the height of the triangle is \(\displaystyle 8.9\) inches.  What is the area of the triangle?

Possible Answers:

\(\displaystyle 55.4\) square inches

\(\displaystyle 51.4\) square inches

\(\displaystyle 53.3\) square inches

\(\displaystyle 52.4\) square inches

\(\displaystyle 53.4\) square inches

Correct answer:

\(\displaystyle 53.4\) square inches

Explanation:

To find the area of a triangle, multiply the base by the height, and divide by two.  The best answer is:

\(\displaystyle 53.4\) square inches

Example Question #31 : Area Of A Triangle

The base of a triangle is \(\displaystyle x\) inches, and the height of the triangle is \(\displaystyle y\) inches.  What is the area of the triangle?

Possible Answers:

\(\displaystyle \frac{2xy}{2}\) square inches

\(\displaystyle \frac{3x}{2}\) square inches

\(\displaystyle \frac{y}{2}\) square inches

\(\displaystyle \frac{xy}{2}\) square inches

\(\displaystyle \frac{x}{2}\) square inches

Correct answer:

\(\displaystyle \frac{xy}{2}\) square inches

Explanation:

To find the area of a triangle, multiply the base by the height, and divide by two.  The best answer is:

\(\displaystyle \frac{xy}{2}\) square inches

Example Question #111 : Geometry

The base of a triangle is \(\displaystyle t\) inches, and the height of the \(\displaystyle 8\) triangle is  inches.  What is the area of the triangle?

Possible Answers:

\(\displaystyle 8t\) square inches

\(\displaystyle 14t\) square inches

\(\displaystyle 2t\) square inches

\(\displaystyle 4t\) square inches

\(\displaystyle 6t\) square inches

Correct answer:

\(\displaystyle 4t\) square inches

Explanation:

To find the area of a triangle, multiply the base by the height, and divide by two.  The best answer is:

\(\displaystyle 4t\) square inches

Example Question #111 : Area

A triangle with a base of 14 inches and height of 22 inches has an area of what?

Possible Answers:

\(\displaystyle 36in^2\)

\(\displaystyle 84in^2\)

\(\displaystyle 154in^2\)

\(\displaystyle 77in^2\)

\(\displaystyle 308in^2\)

Correct answer:

\(\displaystyle 154in^2\)

Explanation:

The formula for the area of a triangle is:

\(\displaystyle \frac{1}{2} * base * height\)

\(\displaystyle \frac{1}{2} * 14 * 22 = 154in ^2\)

Example Question #32 : Area Of A Triangle

If Joan has a triangle-shaped plot for her garden, with the base measuring 3 ft and the heigh measuring 4 ft, what is the area of her garden?

Possible Answers:

\(\displaystyle 12\) \(\displaystyle ft^2\)

\(\displaystyle 6\) \(\displaystyle ft^2\)

\(\displaystyle 7\) \(\displaystyle ft^2\)

\(\displaystyle 3\) \(\displaystyle ft^2\)

Correct answer:

\(\displaystyle 6\) \(\displaystyle ft^2\)

Explanation:

To find the area of a triangle, use the formula \(\displaystyle \frac{1}{2}(b\times h)\)or \(\displaystyle \frac{b\times h}{2}\)

\(\displaystyle \frac{1}{2}\) \(\displaystyle (3x4)=\) 


\(\displaystyle \frac{1}{2}(12)=\)


\(\displaystyle 6\) square ft

or

\(\displaystyle \frac{(3x4)}{2}=\)

\(\displaystyle \frac{12}{2}=\)


\(\displaystyle 6\) square ft

Example Question #1 : Area Of A Circle

A circle has a circumference of \(\displaystyle \small 6\pi\). What is its area?

Possible Answers:

\(\displaystyle \small 36\pi\)

\(\displaystyle \small 12\pi\)

\(\displaystyle \small 6\pi\)

\(\displaystyle \small 9\pi\)

\(\displaystyle \small 18\pi\)

Correct answer:

\(\displaystyle \small 9\pi\)

Explanation:

To begin, we need to find the radius of the circle. The circumference of a circle is given as follows:

\(\displaystyle \small C = 2\pi r\),

where \(\displaystyle r\) is the radius.

Then, a circle with circumference \(\displaystyle 6\pi\) will have the following radius:

\(\displaystyle 6\pi = 2\pi r\)

\(\displaystyle \small \frac{6\pi}{2\pi}=\frac{2\pi r}{2\pi}\)

\(\displaystyle \small 3=r\)

Using the radius, we can now solve for the area:

\(\displaystyle \small A=\pi r^2\)

\(\displaystyle A=\pi(3)^2\)

\(\displaystyle \small A=9\pi\)

The area of the circle is \(\displaystyle \small 9\pi\).

Example Question #2 : Area Of A Circle

What is the area of a circle with a diameter equal to \(\displaystyle 7\)?

Possible Answers:

\(\displaystyle 24.5\pi\)

\(\displaystyle 98\pi\)

\(\displaystyle 12.25\pi\)

\(\displaystyle 49\pi\)

Correct answer:

\(\displaystyle 12.25\pi\)

Explanation:

If the diameter is 7, then the radius is half of 7, or 3.5.

Plug this value for the radius into the equation for the area of a circle:

\(\displaystyle A=r^2\pi=(3.5)^2\pi=12.25\pi\)

Example Question #3 : Area Of A Circle

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The rectangle in the above figure has length 20 and height 10. What is the area of the orange region?

Possible Answers:

\(\displaystyle 200 + 25 \pi\)

\(\displaystyle 200 + 50 \pi\)

\(\displaystyle 200 + \frac{25}{2} \pi\)

Insufficient information is given to determine the area.

\(\displaystyle 200 + 100 \pi\)

Correct answer:

\(\displaystyle 200 + \frac{25}{2} \pi\)

Explanation:

The orange region is a composite of two figures:

One is a rectangle measuring 20 by 10, which, subsequently, has area

\(\displaystyle 20 \cdot 10 = 200\).

The other is a semicircle with diameter 10, and, subsequently, radius 5. Its area is 

\(\displaystyle \frac{1}{2} \pi \cdot 5^{2} = \frac{25}{2} \pi\).

Add the areas:

\(\displaystyle A = 200 + \frac{25}{2} \pi\)

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