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Basic Geometry : Triangles

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Example Questions

Example Question #32 : How To Find The Area Of A Right Triangle

Find the area of a right triangle with leg lengths of $\frac{2}{3}$ $\displaystyle \frac{2}{3}$ and $\frac{1}{4}$ $\displaystyle \frac{1}{4}$.

Possible Answers:

$\frac{1}{12}$ $\displaystyle \frac{1}{12}$

$\frac{1}{4}$ $\displaystyle \frac{1}{4}$

$\frac{1}{6}$ $\displaystyle \frac{1}{6}$

$\frac{1}{24}$ $\displaystyle \frac{1}{24}$

Correct answer:

$\frac{1}{12}$ $\displaystyle \frac{1}{12}$

Explanation:

Recall how to find the area of a right triangle:

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

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.

$\text{Area}=\frac{1}{2}\left(\frac{2}{3} \times \frac{1}{4}\right)$ $\displaystyle \text{Area}=\frac{1}{2}\left(\frac{2}{3} \times \frac{1}{4}\right)$

Simplify.

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

Solve.

$\text{Area}=\frac{2}{24}$ $\displaystyle \text{Area}=\frac{2}{24}$

Reduce.

$\text{Area}=\frac{1}{12}$ $\displaystyle \text{Area}=\frac{1}{12}$

Report an Error

Example Question #33 : How To Find The Area Of A Right Triangle

Find the area of a right triangle with leg lengths of $\displaystyle 12$ and $\displaystyle 15$.

Possible Answers:

150 $\displaystyle 150$

$\displaystyle 90$

180 $\displaystyle 180$

120 $\displaystyle 120$

Correct answer:

$\displaystyle 90$

Explanation:

Recall how to find the area of a right triangle:

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

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.

$\text{Area}=\frac{1}{2}(12 \times 15)$ $\displaystyle \text{Area}=\frac{1}{2}(12 \times 15)$

Simplify.

$\text{Area}=\frac{1}{2}(180)$ $\displaystyle \text{Area}=\frac{1}{2}(180)$

Solve.

$\text{Area}=90$ $\displaystyle \text{Area}=90$

Report an Error

Example Question #34 : How To Find The Area Of A Right Triangle

Find the area of a right triangle with leg lengths of $\displaystyle 3$ and $\displaystyle 10$.

Possible Answers:

$\displaystyle 27$

$\displaystyle 15$

$\displaystyle 30$

$\displaystyle 12$

Correct answer:

$\displaystyle 15$

Explanation:

Recall how to find the area of a right triangle:

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

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.

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

Simplify.

$\text{Area}=\frac{1}{2}(30)$ $\displaystyle \text{Area}=\frac{1}{2}(30)$

Solve.

$\text{Area}=15$ $\displaystyle \text{Area}=15$

Report an Error

Example Question #35 : How To Find The Area Of A Right Triangle

Find the area of a right triangle with leg lengths of $\displaystyle 5$ and $\displaystyle 12$.

Possible Answers:

$\displaystyle 20$

$\displaystyle 60$

$\displaystyle 30$

$\displaystyle 40$

Correct answer:

$\displaystyle 30$

Explanation:

Recall how to find the area of a right triangle:

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

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.

$\text{Area}=\frac{1}{2}(5 \times 12)$ $\displaystyle \text{Area}=\frac{1}{2}(5 \times 12)$

Simplify.

$\text{Area}=\frac{1}{2}(60)$ $\displaystyle \text{Area}=\frac{1}{2}(60)$

Solve.

$\text{Area}=30$ $\displaystyle \text{Area}=30$

Report an Error

Example Question #36 : How To Find The Area Of A Right Triangle

Find the area of a right triangle with leg lengths of $\displaystyle 15$ and $\displaystyle 10$.

Possible Answers:

$\displaystyle 65$

$\displaystyle 85$

$\displaystyle 55$

$\displaystyle 75$

Correct answer:

$\displaystyle 75$

Explanation:

Recall how to find the area of a right triangle:

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

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.

$\text{Area}=\frac{1}{2}(10 \times 15)$ $\displaystyle \text{Area}=\frac{1}{2}(10 \times 15)$

Simplify.

$\text{Area}=\frac{1}{2}(150)$ $\displaystyle \text{Area}=\frac{1}{2}(150)$

Solve.

$\text{Area}=75$ $\displaystyle \text{Area}=75$

Report an Error

Example Question #37 : How To Find The Area Of A Right Triangle

Find the area of a right triangle with leg lengths of $\displaystyle 50$ and $\displaystyle 12$.

Possible Answers:

300 $\displaystyle 300$

600 $\displaystyle 600$

150 $\displaystyle 150$

900 $\displaystyle 900$

Correct answer:

300 $\displaystyle 300$

Explanation:

Recall how to find the area of a right triangle:

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

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.

$\text{Area}=\frac{1}{2}(50 \times 12)$ $\displaystyle \text{Area}=\frac{1}{2}(50 \times 12)$

Simplify.

$\text{Area}=\frac{1}{2}(600)$ $\displaystyle \text{Area}=\frac{1}{2}(600)$

Solve.

$\text{Area}=300$ $\displaystyle \text{Area}=300$

Report an Error

Example Question #1413 : Basic Geometry

Find the area of a right triangle with leg lengths of $\displaystyle 24$ and $\displaystyle 12$.

Possible Answers:

288 $\displaystyle 288$

108 $\displaystyle 108$

$\displaystyle 96$

144 $\displaystyle 144$

Correct answer:

144 $\displaystyle 144$

Explanation:

Recall how to find the area of a right triangle:

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

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.

$\text{Area}=\frac{1}{2}(24 \times 12)$ $\displaystyle \text{Area}=\frac{1}{2}(24 \times 12)$

Simplify.

$\text{Area}=\frac{1}{2}(288)$ $\displaystyle \text{Area}=\frac{1}{2}(288)$

Solve.

$\text{Area}=144$ $\displaystyle \text{Area}=144$

Report an Error

Example Question #38 : How To Find The Area Of A Right Triangle

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

Possible Answers:

$\displaystyle 1$

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

$\frac{1}{8}$ $\displaystyle \frac{1}{8}$

$\frac{1}{4}$ $\displaystyle \frac{1}{4}$

Correct answer:

$\frac{1}{4}$ $\displaystyle \frac{1}{4}$

Explanation:

Recall how to find the area of a right triangle:

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

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.

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

Simplify.

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

Solve.

$\text{Area}=\frac{1}{4}$ $\displaystyle \text{Area}=\frac{1}{4}$

Report an Error

Example Question #39 : How To Find The Area Of A Right Triangle

Find the area of a right triangle with leg lengths of $\displaystyle 15$ and $\displaystyle 16$.

Possible Answers:

120 $\displaystyle 120$

240 $\displaystyle 240$

132 $\displaystyle 132$

108 $\displaystyle 108$

Correct answer:

120 $\displaystyle 120$

Explanation:

Recall how to find the area of a right triangle:

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

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.

$\text{Area}=\frac{1}{2}(15 \times 16)$ $\displaystyle \text{Area}=\frac{1}{2}(15 \times 16)$

Simplify.

$\text{Area}=\frac{1}{2}(240)$ $\displaystyle \text{Area}=\frac{1}{2}(240)$

Solve.

$\text{Area}=120$ $\displaystyle \text{Area}=120$

Report an Error

Example Question #431 : Triangles

Find the area of a right triangle with leg lengths of $\displaystyle 14$ and $\displaystyle 3$.

Possible Answers:

$\displaystyle 42$

$\displaystyle 35$

$\displaystyle 28$

$\displaystyle 21$

Correct answer:

$\displaystyle 21$

Explanation:

Recall how to find the area of a right triangle:

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

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.

$\text{Area}=\frac{1}{2}(14 \times 3)$ $\displaystyle \text{Area}=\frac{1}{2}(14 \times 3)$

Simplify.

$\text{Area}=\frac{1}{2}(42)$ $\displaystyle \text{Area}=\frac{1}{2}(42)$

Solve.

$\text{Area}=21$ $\displaystyle \text{Area}=21$

Report an Error

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All Basic Geometry Resources

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Basic Geometry : Triangles

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #32 : How To Find The Area Of A Right Triangle

Example Question #33 : How To Find The Area Of A Right Triangle

Example Question #34 : How To Find The Area Of A Right Triangle

Example Question #35 : How To Find The Area Of A Right Triangle

Example Question #36 : How To Find The Area Of A Right Triangle

Example Question #37 : How To Find The Area Of A Right Triangle

Example Question #1413 : Basic Geometry

Example Question #38 : How To Find The Area Of A Right Triangle

Example Question #39 : How To Find The Area Of A Right Triangle

Example Question #431 : Triangles

All Basic Geometry Resources

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