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Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

Example Question #222 : Right Triangles

Find the area of this right triangle:

Area right tri b

Possible Answers:

$\small 30 un^2$

$\small 32 un^2$

$\small 58.31 un^2$

$\small 24 un^2$

$\small 34.99un^2$

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 #223 : Right Triangles

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

Possible Answers:

$\frac{1}{30}$

$\frac{1}{5}$

$\frac{1}{10}$

$\frac{1}{20}$

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 #25 : How To Find The Area Of A Right Triangle

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

Possible Answers:

$\frac{7}{5}$

$\frac{3}{2}$

$\frac{7}{4}$

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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Example Question #1405 : Basic Geometry

Find the area of a right triangle with leg lengths of 0.12 and .

Possible Answers:

0.03

0.12

0.09

0.06

Correct answer:

0.06

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.

$\text{Area}=\frac{1}{2}(0.12 \times 1)$

Simplify.

$\text{Area}=\frac{1}{2}(0.12)$

Solve.

$\text{Area}=0.06$

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Example Question #27 : How To Find The Area Of A Right Triangle

Find the area of a right triangle with leg lengths of and $\frac{4}{5}$ .

Possible Answers:

$\frac{6}{5}$

$\frac{8}{5}$

$\frac{16}{5}$

Correct answer:

$\frac{8}{5}$

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.

$\text{Area}=\frac{1}{2}\left(4 \times \frac{4}{5}\right)$

Simplify.

$\text{Area}=\frac{1}{2}\left( \frac{16}{5}\right)$

Solve.

$\text{Area}= \frac{16}{10}$

Reduce.

$\text{Area}= \frac{8}{5}$

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Example Question #1406 : Basic Geometry

Find the area of a right triangle with leg lengths of 0.25 and .

Possible Answers:

$\frac{1}{4}$

$\frac{1}{2}$

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.

$\text{Area}=\frac{1}{2}(0.25 \times 4)$

Simplify.

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

Solve.

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

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Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #222 : Right Triangles

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 #223 : Right Triangles

Example Question #1404 : Basic Geometry

Example Question #25 : How To Find The Area Of A Right Triangle

Example Question #1405 : Basic Geometry

Example Question #27 : How To Find The Area Of A Right Triangle

Example Question #1406 : Basic Geometry

All Basic Geometry Resources

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