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Basic Geometry : Right Triangles

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Example Questions

Example Question #451 : Geometry

The length of one leg of an equilateral triangle is 6. What is the area of the triangle?

Possible Answers:

$9\sqrt{3}$

Correct answer:

$9\sqrt{3}$

Explanation:

$A=\frac{1}{2}(B)(H)$

The base is equal to 6.

The height of an quilateral triangle is equal to $\frac{B\sqrt{3}}{2}$ , where is the length of the base.

$A=\frac{1}{2}(6)(\frac{6\sqrt{3}}{2})=\frac{1}{2}(6)(3\sqrt{3})=9\sqrt{3}$

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Example Question #1 : How To Find The Area Of A Right Triangle

Find the area of the following right triangle to the nearest integer Finding_area_of_right_triangle

Note: The triangle is not necessarily to scale

Possible Answers:

104

None of the other answers

Correct answer:

Explanation:

The equation used to find the area of a right triangle is: $A = \frac{1}{2}b\cdot h$ where A is the area, b is the base, and h is the height of the triangle. In this question, we are given the height, so we need to figure out the base in order to find the area. Since we know both the height and hypotenuse of the triangle, the quickest way to finding the base is using the pythagorean theorem, $a^{2}+b^{2}=c^{2}$ . a = the height, b = the base, and c = the hypotenuse.

Using the given information, we can write $8^{2} + b^{2} = 13^{2}$ . Solving for b, we get $b^{2} = 105$ or $b \approx 10.25$ . Now that we have both the base and height, we can solve the original equation for the area of the triangle. $A = \frac{1}{2}\cdot10.25\cdot8 = 40.99\approx41$

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Example Question #12 : How To Find The Area Of A Right Triangle

Find the area of this right triangle:

Right triangle perim 2

Possible Answers:

$\small 3.5\sqrt{33}$

$\small 2\sqrt{65}$

$\small 2\sqrt{33}$

$\small \frac{1}{2}\sqrt{132}$

$\small \sqrt{66}$

Correct answer:

$\small 2\sqrt{33}$

Explanation:

The area of a triangle is $\small \frac{1}{2}(base)(height)$ . For a right triangle, we can use the two legs as the base and the height regardless of orientation. Right now we only know one of the legs, and we can solve for the other using Pythagorean Theorem:

$\small \small 4^2 + x^2 = 7^2$

$\small 16 + x^2 = 49$ subtract 16 from both sides

$\small x^2 = 33$

$\small x = \sqrt{33}$ we can see that all of the answers are in radical form, so we do not have to simplify this to a crazy decimal.

Now we have our "base" and "height" and we can plug them into the formula to find the area:

$\small \frac{1}{2}*4*\sqrt{33}$ half of 4 is 2, so our answer is $\small 2\sqrt{33}$ , which we can't simplify any more.

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Example Question #11 : How To Find The Area Of A Right Triangle

Find the area of this right triangle:

Area right tri b

Possible Answers:

$\small 58.31 un^2$

$\small 30 un^2$

$\small 32 un^2$

$\small 24 un^2$

$\small 34.99un^2$

Correct answer:

$\small 24 un^2$

Explanation:

The area of a triangle is found using the formula $\small \frac{1}{2}(base)(height)$ . For a right triangle, we can use the two legs as the base and height regardless of the orientation of the triangle.

In this case, we only know one leg, but we can figure out the other by using the Pythagorean Theorem:

$\small 6^2 + x^2 = 10^2$

$\small 36 + x^2 = 100$ subtract 36 from both sides

$\small x^2 = 64$ take the square root

$\small x = \sqrt{64 } = 8$

Now that we have our "base" and "height," we can substitute them into the formula and find the area:

$\small \frac{1}{2}*8*6 = 4*6 = 24$

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Example Question #12 : How To Find The Area Of A Right Triangle

Find the area of a right triangle whose perpendicular sides are of lengths and .

Possible Answers:

Correct answer:

Explanation:

To find area of this triangle, you must use the formula indicated below.

$A=\frac{1}{2}bh$

where is base and is height. Thus:

$A=\frac{1}{2}(5)(4)=10$

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Example Question #1401 : Basic Geometry

Find the area of a right triangle with leg lengths of and 0.1 .

Possible Answers:

$\frac{1}{2}$

$\frac{1}{5}$

$\frac{1}{10}$

Correct answer:

$\frac{1}{2}$

Explanation:

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Because the legs of the right triangle form a right angle, the legs are also the base and the height.

To find the area of the right triangle, just plug in the values for the lengths of the legs into the equation given above.

$\text{Area}=\frac{1}{2}(10 \times 0.1)$

Simplify.

$\text{Area}=\frac{1}{2}(1)$

Solve.

$\text{Area}=\frac{1}{2}$

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Example Question #21 : How To Find The Area Of A Right Triangle

Find the area of a right triangle with leg lengths of and $\frac{1}{3}$ .

Possible Answers:

Correct answer:

Explanation:

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Because the legs of the right triangle form a right angle, the legs are also the base and the height.

To find the area of the right triangle, just plug in the values for the lengths of the legs into the equation given above.

$\text{Area}=\frac{1}{2} \left( 12 \times \frac{1}{3} \right)$

Simplify.

$\text{Area}=\frac{1}{2} \left( 4 \right)$

Solve.

$\text{Area}=2$

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Example Question #421 : Triangles

Find the area of a right triangle with leg lengths of $\frac{1}{5}$ and $\frac{1}{2}$ .

Possible Answers:

$\frac{1}{30}$

$\frac{1}{10}$

$\frac{1}{20}$

$\frac{1}{5}$

Correct answer:

$\frac{1}{20}$

Explanation:

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Because the legs of the right triangle form a right angle, the legs are also the base and the height.

To find the area of the right triangle, just plug in the values for the lengths of the legs into the equation given above.

$\text{Area}=\frac{1}{2} \left( \frac{1}{5} \times \frac{1}{2} \right )$

Simplify.

$\text{Area}=\frac{1}{2} \left( \frac{1}{10} \right )$

Solve.

$\text{Area}=\frac{1}{20}$

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Example Question #1404 : Basic Geometry

Find the area of a right triangle with leg lengths of and $\frac{1}{3}$ .

Possible Answers:

$\frac{2}{3}$

$\frac{5}{3}$

Correct answer:

$\frac{5}{3}$

Explanation:

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Because the legs of the right triangle form a right angle, the legs are also the base and the height.

To find the area of the right triangle, just plug in the values for the lengths of the legs into the equation given above.

$\text{Area}=\frac{1}{2} \left( 10 \times \frac{1}{3} \right)$

Simplify.

$\text{Area}=\frac{1}{2} \left( \frac{10}{3} \right)$

Solve.

$\text{Area}= \left( \frac{10}{6} \right)$

Reduce.

$\text{Area}= \frac{5}{3}$

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Example Question #422 : Triangles

Find the area of a right triangle with leg lengths of and $\frac{1}{4}$ .

Possible Answers:

$\frac{3}{2}$

$\frac{7}{5}$

$\frac{7}{4}$

Correct answer:

$\frac{7}{4}$

Explanation:

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Because the legs of the right triangle form a right angle, the legs are also the base and the height.

To find the area of the right triangle, just plug in the values for the lengths of the legs into the equation given above.

$\text{Area}=\frac{1}{2}\left(14 \times \frac{1}{4}\right)$

Simplify.

$\text{Area}=\frac{1}{2}\left( \frac{14}{4}\right)$

Solve.

$\text{Area}= \frac{14}{8}$

Reduce.

$\text{Area}= \frac{7}{4}$

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Basic Geometry : Right Triangles

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #451 : Geometry

Example Question #1 : How To Find The Area Of A Right Triangle

Example Question #12 : How To Find The Area Of A Right Triangle

Example Question #11 : How To Find The Area Of A Right Triangle

Example Question #12 : How To Find The Area Of A Right Triangle

Example Question #1401 : Basic Geometry

Example Question #21 : How To Find The Area Of A Right Triangle

Example Question #421 : Triangles

Example Question #1404 : Basic Geometry

Example Question #422 : Triangles

All Basic Geometry Resources

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