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Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

Example Question #1431 : Plane Geometry

Find the area.

Possible Answers:

$\displaystyle 50$

100 $\displaystyle 100$

$\displaystyle 80$

$\displaystyle 75$

Correct answer:

$\displaystyle 50$

Explanation:

Recall how to find the area of a triangle:

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

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

$\text{Area}=\frac{20\times5}{2}=100$ $\displaystyle \text{Area}=\frac{20\times5}{2}=100$

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Example Question #1432 : Plane Geometry

Find the area.

Possible Answers:

2.2875 $\displaystyle 2.2875$

2.4875 $\displaystyle 2.4875$

2.1875 $\displaystyle 2.1875$

2.3875 $\displaystyle 2.3875$

Correct answer:

2.1875 $\displaystyle 2.1875$

Explanation:

Recall how to find the area of a triangle:

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

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

$\text{Area}=\frac{2.5\times1.75}{2}=2.1875$ $\displaystyle \text{Area}=\frac{2.5\times1.75}{2}=2.1875$

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Example Question #1433 : Plane Geometry

Find the area of the triangle.

Possible Answers:

5000 $\displaystyle 5000$

3000 $\displaystyle 3000$

4000 $\displaystyle 4000$

6000 $\displaystyle 6000$

Correct answer:

3000 $\displaystyle 3000$

Explanation:

Recall how to find the area of a triangle:

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

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

$\text{Area}=\frac{100\times60}{2}=300$ $\displaystyle \text{Area}=\frac{100\times60}{2}=300$

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Example Question #1434 : Plane Geometry

Find the area.

Possible Answers:

600 $\displaystyle 600$

800 $\displaystyle 800$

1200 $\displaystyle 1200$

1000 $\displaystyle 1000$

Correct answer:

600 $\displaystyle 600$

Explanation:

Recall how to find the area of a triangle:

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

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

$\text{Area}=\frac{40\times30}{2}=600$ $\displaystyle \text{Area}=\frac{40\times30}{2}=600$

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Example Question #1435 : Plane Geometry

Find the area.

Possible Answers:

360 $\displaystyle 360$

180 $\displaystyle 180$

300 $\displaystyle 300$

240 $\displaystyle 240$

Correct answer:

240 $\displaystyle 240$

Explanation:

Recall how to find the area of a triangle:

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

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

$\text{Area}=\frac{40\times12}{2}=240$ $\displaystyle \text{Area}=\frac{40\times12}{2}=240$

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Example Question #1436 : Plane Geometry

Find the area.

Possible Answers:

800 $\displaystyle 800$

100 $\displaystyle 100$

400 $\displaystyle 400$

600 $\displaystyle 600$

Correct answer:

400 $\displaystyle 400$

Explanation:

Recall how to find the area of a triangle:

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

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

$\text{Area}=\frac{40\times20}{2}=400$ $\displaystyle \text{Area}=\frac{40\times20}{2}=400$

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Example Question #260 : Right Triangles

Find the area.

Possible Answers:

144 $\displaystyle 144$

$72\sqrt3$ $\displaystyle 72\sqrt3$

$\displaystyle 36$

$36\sqrt3$ $\displaystyle 36\sqrt3$

Correct answer:

$72\sqrt3$ $\displaystyle 72\sqrt3$

Explanation:

Recall how to find the area of a triangle:

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

However, the question gives us the length of a height and the length of the hypotenuse. Thus, we will need to use the Pythagorean Theorem to find the length of the base.

$\text{Hypotenuse}^2=\text{base}^2+\text{height}^2$ $\displaystyle \text{Hypotenuse}^2=\text{base}^2+\text{height}^2$

Now, rewrite the equation to solve for the height.

$\text{height}^2=\text{Hypotenuse}^2-\text{base}^2$ $\displaystyle \text{height}^2=\text{Hypotenuse}^2-\text{base}^2$

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

Plug in the values of the hypotenuse and base to find the height.

$\text{height}=\sqrt{24^2-12^2}=\sqrt{432}=12\sqrt3$ $\displaystyle \text{height}=\sqrt{24^2-12^2}=\sqrt{432}=12\sqrt3$

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

$\text{Area}=\frac{12\sqrt3\times12}{2}=72\sqrt3$ $\displaystyle \text{Area}=\frac{12\sqrt3\times12}{2}=72\sqrt3$

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Example Question #1437 : Plane Geometry

Find the area.

Possible Answers:

0.3125 $\displaystyle 0.3125$

1.350 $\displaystyle 1.350$

1.225 $\displaystyle 1.225$

0.875 $\displaystyle 0.875$

Correct answer:

0.3125 $\displaystyle 0.3125$

Explanation:

Recall how to find the area of a triangle:

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

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

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

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Example Question #1432 : Plane Geometry

Find the area.

Possible Answers:

$\frac{169}{}$ $\displaystyle \frac{169}{}$

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

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

169 $\displaystyle 169$

Correct answer:

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

Explanation:

Recall how to find the area of a triangle:

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

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

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

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

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

Substitute in the values of the height and hypotenuse.

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

Simplify.

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

Reduce.

$\text{base}=13\sqrt3$ $\displaystyle \text{base}=13\sqrt3$

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

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

Solve.

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

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

Find the area.

Possible Answers:

$\displaystyle 48$

$4\sqrt3$ $\displaystyle 4\sqrt3$

$\displaystyle 16$

$2\sqrt3$ $\displaystyle 2\sqrt3$

Correct answer:

$2\sqrt3$ $\displaystyle 2\sqrt3$

Explanation:

Recall how to find the area of a triangle:

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

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

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

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

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

Substitute in the values of the height and hypotenuse.

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

Simplify.

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

Reduce.

$\text{base}=2\sqrt3$ $\displaystyle \text{base}=2\sqrt3$

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

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

Solve.

$\text{Area}=2\sqrt3$ $\displaystyle \text{Area}=2\sqrt3$

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Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #1431 : Plane Geometry

Example Question #1432 : Plane Geometry

Example Question #1433 : Plane Geometry

Example Question #1434 : Plane Geometry

Example Question #1435 : Plane Geometry

Example Question #1436 : Plane Geometry

Example Question #260 : Right Triangles

Example Question #1437 : Plane Geometry

Example Question #1432 : Plane Geometry

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

All Basic Geometry Resources

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