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Basic Geometry : Right Triangles

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

Example Question #55 : How To Find The Area Of A Right Triangle

Find the area.

Possible Answers:

1.225

1.350

0.875

0.3125

Correct answer:

0.3125

Explanation:

Recall how to find the area of a triangle:

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

Since this is a right triangle, the base and the height are the two leg lengths given.

$\text{Area}=\frac{2.5\times0.25}{2}=0.3125$

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Example Question #57 : How To Find The Area Of A Right Triangle

Find the area.

Possible Answers:

$\frac{169}{}$

$\frac{13\sqrt3}{2}$

$\frac{169\sqrt3}{2}$

169

Correct answer:

$\frac{169\sqrt3}{2}$

Explanation:

Recall how to find the area of a triangle:

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

Now, we have the height and the hypotenuse from the question. Use the Pythagorean Theorem to find the length of the base.

$\text{hypotenuse}^2=\text{base}^2+\text{height}^2$

$\text{base}^2=\text{hypotenuse}^2-\text{height}^2$

$\text{base}=\sqrt{\text{hypotenuse}^2-\text{height}^2}$

Substitute in the values of the height and hypotenuse.

$\text{base}=\sqrt{26^2-13^2}=\sqrt{507}=13\sqrt3$

Simplify.

$\text{base}=\sqrt{507}$

Reduce.

$\text{base}=13\sqrt3$

Now, substitute in the values of the base and the height to find the area.

$\text{Area}=\frac{13 \times 13\sqrt3}{2}$

Solve.

$\text{Area}=\frac{169\sqrt3}{2}$

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Example Question #58 : How To Find The Area Of A Right Triangle

Find the area.

Possible Answers:

$2\sqrt3$

$4\sqrt3$

Correct answer:

$2\sqrt3$

Explanation:

Recall how to find the area of a triangle:

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

Now, we have the height and the hypotenuse from the question. Use the Pythagorean Theorem to find the length of the base.

$\text{hypotenuse}^2=\text{base}^2+\text{height}^2$

$\text{base}^2=\text{hypotenuse}^2-\text{height}^2$

$\text{base}=\sqrt{\text{hypotenuse}^2-\text{height}^2}$

Substitute in the values of the height and hypotenuse.

$\text{base}=\sqrt{4^2-2^2}$

Simplify.

$\text{base}=\sqrt{12}$

Reduce.

$\text{base}=2\sqrt3$

Now, substitute in the values of the base and the height to find the area.

$\text{Area}=\frac{2 \times 2\sqrt3}{2}$

Solve.

$\text{Area}=2\sqrt3$

Report an Error

Example Question #455 : Triangles

Find the area.

Possible Answers:

$9\sqrt3$

$\frac{9}{2}$

$18\sqrt3$

$\frac{9\sqrt3}{2}$

Correct answer:

$\frac{9\sqrt3}{2}$

Explanation:

Recall how to find the area of a triangle:

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

Now, we have the height and the hypotenuse from the question. Use the Pythagorean Theorem to find the length of the base.

$\text{hypotenuse}^2=\text{base}^2+\text{height}^2$

$\text{base}^2=\text{hypotenuse}^2-\text{height}^2$

$\text{base}=\sqrt{\text{hypotenuse}^2-\text{height}^2}$

Substitute in the values of the height and hypotenuse.

$\text{base}=\sqrt{6^2-3^2}$

Simplify.

$\text{base}=\sqrt{27}$

Reduce.

$\text{base}=3\sqrt3$

Now, substitute in the values of the base and the height to find the area.

$\text{Area}=\frac{3 \times 3\sqrt3}{2}$

Solve.

$\text{Area}\frac{9\sqrt3}{2}$

Report an Error

Example Question #60 : How To Find The Area Of A Right Triangle

Find the area.

Possible Answers:

$12\sqrt3$

$15\sqrt3$

$4\sqrt3$

$8\sqrt3$

Correct answer:

$8\sqrt3$

Explanation:

Recall how to find the area of a triangle:

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

Now, we have the height and the hypotenuse from the question. Use the Pythagorean Theorem to find the length of the base.

$\text{hypotenuse}^2=\text{base}^2+\text{height}^2$

$\text{base}^2=\text{hypotenuse}^2-\text{height}^2$

$\text{base}=\sqrt{\text{hypotenuse}^2-\text{height}^2}$

Substitute in the values of the height and hypotenuse.

$\text{base}=\sqrt{8^2-4^2}$

Simplify.

$\text{base}=\sqrt{48}$

Reduce.

$\text{base}=4\sqrt3$

Now, substitute in the values of the base and the height to find the area.

$\text{Area}=\frac{4 \times 4\sqrt3}{2}$

Solve.

$\text{Area}=8\sqrt3$

Report an Error

Example Question #1441 : Basic Geometry

Find the area.

Possible Answers:

$25\sqrt3$

125

$75\sqrt2$

$\frac{25\sqrt3}{2}$

Correct answer:

$\frac{25\sqrt3}{2}$

Explanation:

Recall how to find the area of a triangle:

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

Now, we have the height and the hypotenuse from the question. Use the Pythagorean Theorem to find the length of the base.

$\text{hypotenuse}^2=\text{base}^2+\text{height}^2$

$\text{base}^2=\text{hypotenuse}^2-\text{height}^2$

$\text{base}=\sqrt{\text{hypotenuse}^2-\text{height}^2}$

Substitute in the values of the height and hypotenuse.

$\text{base}=\sqrt{10^2-5^2}$

Simplify.

$\text{base}=\sqrt{75}$

Reduce.

$\text{base}=5\sqrt3$

Now, substitute in the values of the base and the height to find the area.

$\text{Area}=\frac{5 \times 5\sqrt3}{2}$

Solve.

$\text{Area}=\frac{25\sqrt3}{2}$

Report an Error

Example Question #1442 : Basic Geometry

Find the area.

Possible Answers:

$64\sqrt3$

$48\sqrt3$

$60\sqrt3$

$32\sqrt3$

Correct answer:

$32\sqrt3$

Explanation:

Recall how to find the area of a triangle:

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

Now, we have the height and the hypotenuse from the question. Use the Pythagorean Theorem to find the length of the base.

$\text{hypotenuse}^2=\text{base}^2+\text{height}^2$

$\text{base}^2=\text{hypotenuse}^2-\text{height}^2$

$\text{base}=\sqrt{\text{hypotenuse}^2-\text{height}^2}$

Substitute in the values of the height and hypotenuse.

$\text{base}=\sqrt{16^2-8^2}$

Simplify.

$\text{base}=\sqrt{192}$

Reduce.

$\text{base}=8\sqrt3$

Now, substitute in the values of the base and the height to find the area.

$\text{Area}=\frac{8 \times 8\sqrt3}{2}$

Solve.

$\text{Area}=32\sqrt3$

Report an Error

Example Question #261 : Right Triangles

Find the area.

Possible Answers:

$\frac{81\sqrt3}{2}$

$99\sqrt3$

$81\sqrt3$

$\frac{117\sqrt3}{2}$

Correct answer:

$\frac{81\sqrt3}{2}$

Explanation:

Recall how to find the area of a triangle:

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

Now, we have the height and the hypotenuse from the question. Use the Pythagorean Theorem to find the length of the base.

$\text{hypotenuse}^2=\text{base}^2+\text{height}^2$

$\text{base}^2=\text{hypotenuse}^2-\text{height}^2$

$\text{base}=\sqrt{\text{hypotenuse}^2-\text{height}^2}$

Substitute in the values of the height and hypotenuse.

$\text{base}=\sqrt{18^2-9^2}$

Simplify.

$\text{base}=\sqrt{243}$

Reduce.

$\text{base}=9\sqrt3$

Now, substitute in the values of the base and the height to find the area.

$\text{Area}=\frac{9 \times 9\sqrt3}{2}$

Solve.

$\text{Area}=\frac{81\sqrt3}{2}$

Report an Error

Example Question #1441 : Plane Geometry

Find the area.

Possible Answers:

$110\sqrt3$

$\frac{121\sqrt3}{2}$

$121\sqrt3$

$243\sqrt3$

Correct answer:

$\frac{121\sqrt3}{2}$

Explanation:

Recall how to find the area of a triangle:

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

Now, we have the height and the hypotenuse from the question. Use the Pythagorean Theorem to find the length of the base.

$\text{hypotenuse}^2=\text{base}^2+\text{height}^2$

$\text{base}^2=\text{hypotenuse}^2-\text{height}^2$

$\text{base}=\sqrt{\text{hypotenuse}^2-\text{height}^2}$

Substitute in the values of the height and hypotenuse.

$\text{base}=\sqrt{22^2-11^2}$

Simplify.

$\text{base}=\sqrt{363}$

Reduce.

$\text{base}=11\sqrt3$

Now, substitute in the values of the base and the height to find the area.

$\text{Area}=\frac{11 \times 11\sqrt3}{2}$

Solve.

$\text{Area}=\frac{121\sqrt3}{2}$

Report an Error

Example Question #1445 : Basic Geometry

Find the area.

Possible Answers:

144

$72\sqrt3$

$144\sqrt3$

$36\sqrt3$

Correct answer:

$72\sqrt3$

Explanation:

Recall how to find the area of a triangle:

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

Now, we have the height and the hypotenuse from the question. Use the Pythagorean Theorem to find the length of the base.

$\text{hypotenuse}^2=\text{base}^2+\text{height}^2$

$\text{base}^2=\text{hypotenuse}^2-\text{height}^2$

$\text{base}=\sqrt{\text{hypotenuse}^2-\text{height}^2}$

Substitute in the values of the height and hypotenuse.

$\text{base}=\sqrt{24^2-12^2}$

Simplify.

$\text{base}=\sqrt{432}$

Reduce.

$\text{base}=12\sqrt3$

Now, substitute in the values of the base and the height to find the area.

$\text{Area}=\frac{12 \times 12\sqrt3}{2}$

Solve.

$\text{Area}=72\sqrt3$

Report an Error

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All Basic Geometry Resources

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Basic Geometry : Right Triangles

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #55 : How To Find The Area Of A Right Triangle

Example Question #57 : How To Find The Area Of A Right Triangle

Example Question #58 : How To Find The Area Of A Right Triangle

Example Question #455 : Triangles

Example Question #60 : How To Find The Area Of A Right Triangle

Example Question #1441 : Basic Geometry

Example Question #1442 : Basic Geometry

Example Question #261 : Right Triangles

Example Question #1441 : Plane Geometry

Example Question #1445 : Basic Geometry

All Basic Geometry Resources

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