Basic Geometry : Basic Geometry

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

Example Question #781 : Plane Geometry

Find the area of the square.

12

Possible Answers:

Correct answer:

Explanation:

The diagonal of a square is also the hypotenuse of a right isosceles triangle that has the sides of the square as its legs.

Thus, we can use the Pythagorean Theorem to find the length of the sides of the square.

Recall how to find the area of a square.

Now, substitute in the value of the diagonal to find the area of the square.

Solve.

Example Question #782 : Plane Geometry

Find the area of a square inscribed in a circle that has a diameter of .

Possible Answers:

Correct answer:

Explanation:

13

Notice that when a squre is inscribed in a circle, the diameter of the circle is also the diagonal of the square.

Thus, we can figure out the diagonal of the square.

Recall that the diagonal of a square is also the hypotenuse of a right isosceles triangle that has the sides of the square as its legs. We can then use the Pythagorean Theorem to find the length of the sides of the square.

Now, recall the formula for the area of a square.

Thus, we can also write the following formula to find the area of the square:'

Plug in the value of the diagonal to find the area of the square.

Example Question #121 : Squares

Find the area of a square inscribed in a circle that has a diameter of .

Possible Answers:

Correct answer:

Explanation:

13

Notice that when a squre is inscribed in a circle, the diameter of the circle is also the diagonal of the square.

Thus, we can figure out the diagonal of the square.

Recall that the diagonal of a square is also the hypotenuse of a right isosceles triangle that has the sides of the square as its legs. We can then use the Pythagorean Theorem to find the length of the sides of the square.

Now, recall the formula for the area of a square.

Thus, we can also write the following formula to find the area of the square:'

Plug in the value of the diagonal to find the area of the square.

Example Question #784 : Plane Geometry

Find the area of a square inscribed in a circle that has a diameter of .

Possible Answers:

Correct answer:

Explanation:

13

Notice that when a squre is inscribed in a circle, the diameter of the circle is also the diagonal of the square.

Thus, we can figure out the diagonal of the square.

Recall that the diagonal of a square is also the hypotenuse of a right isosceles triangle that has the sides of the square as its legs. We can then use the Pythagorean Theorem to find the length of the sides of the square.

Now, recall the formula for the area of a square.

Thus, we can also write the following formula to find the area of the square:'

Plug in the value of the diagonal to find the area of the square.

Example Question #781 : Basic Geometry

Find the area of a square inscribed in a circle that has a diameter of .

Possible Answers:

Correct answer:

Explanation:

13

Notice that when a squre is inscribed in a circle, the diameter of the circle is also the diagonal of the square.

Thus, we can figure out the diagonal of the square.

Recall that the diagonal of a square is also the hypotenuse of a right isosceles triangle that has the sides of the square as its legs. We can then use the Pythagorean Theorem to find the length of the sides of the square.

Now, recall the formula for the area of a square.

Thus, we can also write the following formula to find the area of the square:'

Plug in the value of the diagonal to find the area of the square.

Example Question #786 : Basic Geometry

Find the area of a square inscribed in a circle that has a diameter of .

Possible Answers:

Correct answer:

Explanation:

13

Notice that when a squre is inscribed in a circle, the diameter of the circle is also the diagonal of the square.

Thus, we can figure out the diagonal of the square.

Recall that the diagonal of a square is also the hypotenuse of a right isosceles triangle that has the sides of the square as its legs. We can then use the Pythagorean Theorem to find the length of the sides of the square.

Now, recall the formula for the area of a square.

Thus, we can also write the following formula to find the area of the square:'

Plug in the value of the diagonal to find the area of the square.

Example Question #787 : Basic Geometry

Find the area of a square inscribed in a circle with a diameter of .

Possible Answers:

Correct answer:

Explanation:

13

Notice that when a squre is inscribed in a circle, the diameter of the circle is also the diagonal of the square.

Thus, we can figure out the diagonal of the square.

Recall that the diagonal of a square is also the hypotenuse of a right isosceles triangle that has the sides of the square as its legs. We can then use the Pythagorean Theorem to find the length of the sides of the square.

Now, recall the formula for the area of a square.

Thus, we can also write the following formula to find the area of the square:'

Plug in the value of the diagonal to find the area of the square.

Example Question #788 : Basic Geometry

Find the area of a square inscribed in a circle that has a diameter of .

Possible Answers:

Correct answer:

Explanation:

13

Notice that when a squre is inscribed in a circle, the diameter of the circle is also the diagonal of the square.

Thus, we can figure out the diagonal of the square.

Recall that the diagonal of a square is also the hypotenuse of a right isosceles triangle that has the sides of the square as its legs. We can then use the Pythagorean Theorem to find the length of the sides of the square.

Now, recall the formula for the area of a square.

Thus, we can also write the following formula to find the area of the square:'

Plug in the value of the diagonal to find the area of the square.

Example Question #782 : Basic Geometry

Find the area of a square inscribed in a circle that has a diameter of .

Possible Answers:

Correct answer:

Explanation:

13

Notice that when a squre is inscribed in a circle, the diameter of the circle is also the diagonal of the square.

Thus, we can figure out the diagonal of the square.

Recall that the diagonal of a square is also the hypotenuse of a right isosceles triangle that has the sides of the square as its legs. We can then use the Pythagorean Theorem to find the length of the sides of the square.

Now, recall the formula for the area of a square.

Thus, we can also write the following formula to find the area of the square:'

Plug in the value of the diagonal to find the area of the square.

Example Question #790 : Basic Geometry

Find the area of a square inscribed in a circle that has a diameter of .

Possible Answers:

Correct answer:

Explanation:

13

Notice that when a squre is inscribed in a circle, the diameter of the circle is also the diagonal of the square.

Thus, we can figure out the diagonal of the square.

Recall that the diagonal of a square is also the hypotenuse of a right isosceles triangle that has the sides of the square as its legs. We can then use the Pythagorean Theorem to find the length of the sides of the square.

Now, recall the formula for the area of a square.

Thus, we can also write the following formula to find the area of the square:'

Plug in the value of the diagonal to find the area of the square.

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