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Basic Geometry : Basic Geometry

Study concepts, example questions & explanations for Basic Geometry

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9 Diagnostic Tests 164 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #81 : Radius

A circle is inscribed in a square that has side lengths of $\displaystyle 10$. Find the area of the circle.

Possible Answers:

$25\pi$ $\displaystyle 25\pi$

$10\pi$ $\displaystyle 10\pi$

$50\pi$ $\displaystyle 50\pi$

$100\pi$ $\displaystyle 100\pi$

Correct answer:

$25\pi$ $\displaystyle 25\pi$

Explanation:

Notice that when a circle is inscribed in a square, the length of the side of the square is the same as the diameter of a circle.

Recall how to find the area of a circle:

$\text{Area}=\pi\times\text{radius}^2$ $\displaystyle \text{Area}=\pi\times\text{radius}^2$

Now, recall the relationship between the radius and the diameter.

$\text{Radius}=\frac{\text{diameter}}{2}$ $\displaystyle \text{Radius}=\frac{\text{diameter}}{2}$

Use the given information to find the radius.

$\text{Radius}=\frac{10}{2}$ $\displaystyle \text{Radius}=\frac{10}{2}$

Simplify.

$\text{Radius}=5$ $\displaystyle \text{Radius}=5$

Now, substitute in the value of the radius to find the area of the circle.

$\text{Area}=\pi\times 5^2$ $\displaystyle \text{Area}=\pi\times 5^2$

Solve.

$\text{Area}=25\pi$ $\displaystyle \text{Area}=25\pi$

Report an Error

Example Question #81 : Radius

A circle is inscribed in a square that has side lengths of $\displaystyle 8$. Find the area of the circle.

Possible Answers:

$64\pi$ $\displaystyle 64\pi$

$32\pi$ $\displaystyle 32\pi$

$128\pi$ $\displaystyle 128\pi$

$16\pi$ $\displaystyle 16\pi$

Correct answer:

$16\pi$ $\displaystyle 16\pi$

Explanation:

Notice that when a circle is inscribed in a square, the length of the side of the square is the same as the diameter of a circle.

Recall how to find the area of a circle:

$\text{Area}=\pi\times\text{radius}^2$ $\displaystyle \text{Area}=\pi\times\text{radius}^2$

Now, recall the relationship between the radius and the diameter.

$\text{Radius}=\frac{\text{diameter}}{2}$ $\displaystyle \text{Radius}=\frac{\text{diameter}}{2}$

Use the given information to find the radius.

$\text{Radius}=\frac{8}{2}$ $\displaystyle \text{Radius}=\frac{8}{2}$

Simplify.

$\text{Radius}=4$ $\displaystyle \text{Radius}=4$

Now, substitute in the value of the radius to find the area of the circle.

$\text{Area}=\pi\times 4^2$ $\displaystyle \text{Area}=\pi\times 4^2$

Solve.

$\text{Area}=16\pi$ $\displaystyle \text{Area}=16\pi$

Report an Error

Example Question #81 : Basic Geometry

A circle is inscribed in a square that has side lengths of $\displaystyle 6$. Find the area of the circle.

Possible Answers:

$9\pi$ $\displaystyle 9\pi$

$12\pi$ $\displaystyle 12\pi$

$18\pi$ $\displaystyle 18\pi$

$36\pi$ $\displaystyle 36\pi$

Correct answer:

$9\pi$ $\displaystyle 9\pi$

Explanation:

Notice that when a circle is inscribed in a square, the length of the side of the square is the same as the diameter of a circle.

Recall how to find the area of a circle:

$\text{Area}=\pi\times\text{radius}^2$ $\displaystyle \text{Area}=\pi\times\text{radius}^2$

Now, recall the relationship between the radius and the diameter.

$\text{Radius}=\frac{\text{diameter}}{2}$ $\displaystyle \text{Radius}=\frac{\text{diameter}}{2}$

Use the given information to find the radius.

$\text{Radius}=\frac{6}{2}$ $\displaystyle \text{Radius}=\frac{6}{2}$

Simplify.

$\text{Radius}=3$ $\displaystyle \text{Radius}=3$

Now, substitute in the value of the radius to find the area of the circle.

$\text{Area}=\pi\times 3^2$ $\displaystyle \text{Area}=\pi\times 3^2$

Solve.

$\text{Area}=9\pi$ $\displaystyle \text{Area}=9\pi$

Report an Error

Example Question #84 : Radius

Find the area of a circle that is inscribed in a square with side lengths of $\displaystyle 4$.

Possible Answers:

$12\pi$ $\displaystyle 12\pi$

$16\pi$ $\displaystyle 16\pi$

$4\pi$ $\displaystyle 4\pi$

$8\pi$ $\displaystyle 8\pi$

Correct answer:

$4\pi$ $\displaystyle 4\pi$

Explanation:

Notice that when a circle is inscribed in a square, the length of the side of the square is the same as the diameter of a circle.

Recall how to find the area of a circle:

$\text{Area}=\pi\times\text{radius}^2$ $\displaystyle \text{Area}=\pi\times\text{radius}^2$

Now, recall the relationship between the radius and the diameter.

$\text{Radius}=\frac{\text{diameter}}{2}$ $\displaystyle \text{Radius}=\frac{\text{diameter}}{2}$

Use the given information to find the radius.

$\text{Radius}=\frac{4}{2}$ $\displaystyle \text{Radius}=\frac{4}{2}$

Simplify.

$\text{Radius}=2$ $\displaystyle \text{Radius}=2$

Now, substitute in the value of the radius to find the area of the circle.

$\text{Area}=\pi\times 2^2$ $\displaystyle \text{Area}=\pi\times 2^2$

Solve.

$\text{Area}=4\pi$ $\displaystyle \text{Area}=4\pi$

Report an Error

Example Question #85 : Radius

Find the area of a circle that is inscribed in a square that has side lengths of $\displaystyle 14$.

Possible Answers:

$28\pi$ $\displaystyle 28\pi$

$49\pi$ $\displaystyle 49\pi$

$63\pi$ $\displaystyle 63\pi$

$164\pi$ $\displaystyle 164\pi$

Correct answer:

$49\pi$ $\displaystyle 49\pi$

Explanation:

Notice that when a circle is inscribed in a square, the length of the side of the square is the same as the diameter of a circle.

Recall how to find the area of a circle:

$\text{Area}=\pi\times\text{radius}^2$ $\displaystyle \text{Area}=\pi\times\text{radius}^2$

Now, recall the relationship between the radius and the diameter.

$\text{Radius}=\frac{\text{diameter}}{2}$ $\displaystyle \text{Radius}=\frac{\text{diameter}}{2}$

Use the given information to find the radius.

$\text{Radius}=\frac{14}{2}$ $\displaystyle \text{Radius}=\frac{14}{2}$

Simplify.

$\text{Radius}=7$ $\displaystyle \text{Radius}=7$

Now, substitute in the value of the radius to find the area of the circle.

$\text{Area}=\pi\times 7^2$ $\displaystyle \text{Area}=\pi\times 7^2$

Solve.

$\text{Area}=49\pi$ $\displaystyle \text{Area}=49\pi$

Report an Error

Example Question #86 : Radius

Find the area of a circle that is inscribed in a square that has side lengths of $\displaystyle 16$.

Possible Answers:

$128\pi$ $\displaystyle 128\pi$

$64\pi$ $\displaystyle 64\pi$

$32\pi$ $\displaystyle 32\pi$

$256\pi$ $\displaystyle 256\pi$

Correct answer:

$64\pi$ $\displaystyle 64\pi$

Explanation:

Notice that when a circle is inscribed in a square, the length of the side of the square is the same as the diameter of a circle.

Recall how to find the area of a circle:

$\text{Area}=\pi\times\text{radius}^2$ $\displaystyle \text{Area}=\pi\times\text{radius}^2$

Now, recall the relationship between the radius and the diameter.

$\text{Radius}=\frac{\text{diameter}}{2}$ $\displaystyle \text{Radius}=\frac{\text{diameter}}{2}$

Use the given information to find the radius.

$\text{Radius}=\frac{16}{2}$ $\displaystyle \text{Radius}=\frac{16}{2}$

Simplify.

$\text{Radius}=8$ $\displaystyle \text{Radius}=8$

Now, substitute in the value of the radius to find the area of the circle.

$\text{Area}=\pi\times 8^2$ $\displaystyle \text{Area}=\pi\times 8^2$

Solve.

$\text{Area}=64\pi$ $\displaystyle \text{Area}=64\pi$

Report an Error

Example Question #87 : Radius

Find the area of a circle that is inscribed in a square that has side lengths of $\displaystyle 18$.

Possible Answers:

$18\pi$ $\displaystyle 18\pi$

$54\pi$ $\displaystyle 54\pi$

$81\pi$ $\displaystyle 81\pi$

$36\pi$ $\displaystyle 36\pi$

Correct answer:

$81\pi$ $\displaystyle 81\pi$

Explanation:

Notice that when a circle is inscribed in a square, the length of the side of the square is the same as the diameter of a circle.

Recall how to find the area of a circle:

$\text{Area}=\pi\times\text{radius}^2$ $\displaystyle \text{Area}=\pi\times\text{radius}^2$

Now, recall the relationship between the radius and the diameter.

$\text{Radius}=\frac{\text{diameter}}{2}$ $\displaystyle \text{Radius}=\frac{\text{diameter}}{2}$

Use the given information to find the radius.

$\text{Radius}=\frac{18}{2}$ $\displaystyle \text{Radius}=\frac{18}{2}$

Simplify.

$\text{Radius}=9$ $\displaystyle \text{Radius}=9$

Now, substitute in the value of the radius to find the area of the circle.

$\text{Area}=\pi\times 9^2$ $\displaystyle \text{Area}=\pi\times 9^2$

Solve.

$\text{Area}=81\pi$ $\displaystyle \text{Area}=81\pi$

Report an Error

Example Question #82 : Radius

Find the area of a circle that is inscribed in a square that has side lengths of $\displaystyle 20$.

Possible Answers:

$200\pi$ $\displaystyle 200\pi$

$400\pi$ $\displaystyle 400\pi$

$100\pi$ $\displaystyle 100\pi$

$300\pi$ $\displaystyle 300\pi$

Correct answer:

$100\pi$ $\displaystyle 100\pi$

Explanation:

Notice that when a circle is inscribed in a square, the length of the side of the square is the same as the diameter of a circle.

Recall how to find the area of a circle:

$\text{Area}=\pi\times\text{radius}^2$ $\displaystyle \text{Area}=\pi\times\text{radius}^2$

Now, recall the relationship between the radius and the diameter.

$\text{Radius}=\frac{\text{diameter}}{2}$ $\displaystyle \text{Radius}=\frac{\text{diameter}}{2}$

Use the given information to find the radius.

$\text{Radius}=\frac{20}{2}$ $\displaystyle \text{Radius}=\frac{20}{2}$

Simplify.

$\text{Radius}=10$ $\displaystyle \text{Radius}=10$

Now, substitute in the value of the radius to find the area of the circle.

$\text{Area}=\pi\times 10^2$ $\displaystyle \text{Area}=\pi\times 10^2$

Solve.

$\text{Area}=100\pi$ $\displaystyle \text{Area}=100\pi$

Report an Error

Example Question #81 : Circles

Find the area of a circle that is inscribed in a square that has side lengths of $\displaystyle 22$.

Possible Answers:

$121\pi$ $\displaystyle 121\pi$

$100\pi$ $\displaystyle 100\pi$

$144\pi$ $\displaystyle 144\pi$

$169\pi$ $\displaystyle 169\pi$

Correct answer:

$121\pi$ $\displaystyle 121\pi$

Explanation:

Notice that when a circle is inscribed in a square, the length of the side of the square is the same as the diameter of a circle.

Recall how to find the area of a circle:

$\text{Area}=\pi\times\text{radius}^2$ $\displaystyle \text{Area}=\pi\times\text{radius}^2$

Now, recall the relationship between the radius and the diameter.

$\text{Radius}=\frac{\text{diameter}}{2}$ $\displaystyle \text{Radius}=\frac{\text{diameter}}{2}$

Use the given information to find the radius.

$\text{Radius}=\frac{22}{2}$ $\displaystyle \text{Radius}=\frac{22}{2}$

Simplify.

$\text{Radius}=11$ $\displaystyle \text{Radius}=11$

Now, substitute in the value of the radius to find the area of the circle.

$\text{Area}=\pi\times 11^2$ $\displaystyle \text{Area}=\pi\times 11^2$

Solve.

$\text{Area}=121\pi$ $\displaystyle \text{Area}=121\pi$

Report an Error

Example Question #82 : Plane Geometry

Find the area of a circle that is inscribed in a square that has side lengths of $\displaystyle 24$.

Possible Answers:

$120\pi$ $\displaystyle 120\pi$

$132\pi$ $\displaystyle 132\pi$

$165\pi$ $\displaystyle 165\pi$

$144\pi$ $\displaystyle 144\pi$

Correct answer:

$144\pi$ $\displaystyle 144\pi$

Explanation:

Notice that when a circle is inscribed in a square, the length of the side of the square is the same as the diameter of a circle.

Recall how to find the area of a circle:

$\text{Area}=\pi\times\text{radius}^2$ $\displaystyle \text{Area}=\pi\times\text{radius}^2$

Now, recall the relationship between the radius and the diameter.

$\text{Radius}=\frac{\text{diameter}}{2}$ $\displaystyle \text{Radius}=\frac{\text{diameter}}{2}$

Use the given information to find the radius.

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

Simplify.

$\text{Radius}=12$ $\displaystyle \text{Radius}=12$

Now, substitute in the value of the radius to find the area of the circle.

$\text{Area}=\pi\times 12^2$ $\displaystyle \text{Area}=\pi\times 12^2$

Solve.

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

Report an Error

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Basic Geometry : Basic Geometry

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #81 : Radius

Example Question #81 : Radius

Example Question #81 : Basic Geometry

Example Question #84 : Radius

Example Question #85 : Radius

Example Question #86 : Radius

Example Question #87 : Radius

Example Question #82 : Radius

Example Question #81 : Circles

Example Question #82 : Plane Geometry

All Basic Geometry Resources

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