QuestionFind the area of a square inscribed in a circle with a diameter of 4. Options: A. 2 B. 4 C. 8 D. 9 E. 16

Studdy Solution

STEP 1

Assumptions1. The square is inscribed in the circle, which means that the diameter of the circle is equal to the diagonal of the square. . The diameter of the circle is given as4 units.
3. We need to find the area of the square.

STEP 2

The diagonal of a square splits the square into two congruent right triangles. By the Pythagorean theorem, the square of the diagonal (d) is equal to the sum of the squares of the sides (a) of the square.
$d^2 = a^2 + a^2$

STEP 3

Since the square has equal sides, the equation can be simplified to $d^2 =2a^2$

STEP 4

We know that the diagonal of the square is equal to the diameter of the circle, which is4 units. Substitute this value into the equation $4^2 =2a^2$

STEP 5

olve the equation for the side length (a) of the square $a^2 = \frac{4^2}{2}$

STEP 6

Calculate the side length of the square $a^2 = \frac{16}{2} =8$

STEP 7

The area (A) of a square is given by the square of the side length (a):
$A = a^2$

STEP 8

Substitute the value of the side length into the equation to find the area of the square $A =8$ So, the area of the square is8 square units. The correct answer is C.8.

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QuestionFind the area of a square inscribed in a circle with a diameter of 4. Options: A. 2 B. 4 C. 8 D. 9 E. 16

Studdy Solution

STEP 1

Assumptions1. The square is inscribed in the circle, which means that the diameter of the circle is equal to the diagonal of the square. . The diameter of the circle is given as4 units.
3. We need to find the area of the square.

STEP 2

The diagonal of a square splits the square into two congruent right triangles. By the Pythagorean theorem, the square of the diagonal (d) is equal to the sum of the squares of the sides (a) of the square.
$d^2 = a^2 + a^2$

STEP 3

Since the square has equal sides, the equation can be simplified to $d^2 =2a^2$

STEP 4

We know that the diagonal of the square is equal to the diameter of the circle, which is4 units. Substitute this value into the equation $4^2 =2a^2$

STEP 5

olve the equation for the side length (a) of the square $a^2 = \frac{4^2}{2}$

STEP 6

Calculate the side length of the square $a^2 = \frac{16}{2} =8$

STEP 7

The area (A) of a square is given by the square of the side length (a):
$A = a^2$

STEP 8

Substitute the value of the side length into the equation to find the area of the square $A =8$ So, the area of the square is8 square units. The correct answer is C.8.

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QuestionFind the area of a square inscribed in a circle with a diameter of 4. Options: A. 2 B. 4 C. 8 D. 9 E. 16

Studdy Solution

STEP 1

Assumptions1. The square is inscribed in the circle, which means that the diameter of the circle is equal to the diagonal of the square. . The diameter of the circle is given as4 units.3. We need to find the area of the square.

STEP 2

The diagonal of a square splits the square into two congruent right triangles. By the Pythagorean theorem, the square of the diagonal (d) is equal to the sum of the squares of the sides (a) of the square.d2=a2+a2d^2 = a^2 + a^2d2=a2+a2

STEP 3

Since the square has equal sides, the equation can be simplified tod2=2a2d^2 =2a^2d2=2a2

STEP 4

We know that the diagonal of the square is equal to the diameter of the circle, which is4 units. Substitute this value into the equation42=2a24^2 =2a^242=2a2

STEP 5

olve the equation for the side length (a) of the squarea2=422a^2 = \frac{4^2}{2}a2=242​

STEP 6

Calculate the side length of the squarea2=162=8a^2 = \frac{16}{2} =8a2=216​=8

STEP 7

The area (A) of a square is given by the square of the side length (a):A=a2A = a^2A=a2

STEP 8

Substitute the value of the side length into the equation to find the area of the squareA=8A =8A=8So, the area of the square is8 square units. The correct answer is C.8.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Assumptions1. The square is inscribed in the circle, which means that the diameter of the circle is equal to the diagonal of the square. . The diameter of the circle is given as4 units.
3. We need to find the area of the square.

The diagonal of a square splits the square into two congruent right triangles. By the Pythagorean theorem, the square of the diagonal (d) is equal to the sum of the squares of the sides (a) of the square.
$d^2 = a^2 + a^2$

Since the square has equal sides, the equation can be simplified to $d^2 =2a^2$

We know that the diagonal of the square is equal to the diameter of the circle, which is4 units. Substitute this value into the equation $4^2 =2a^2$

olve the equation for the side length (a) of the square $a^2 = \frac{4^2}{2}$

Calculate the side length of the square $a^2 = \frac{16}{2} =8$

The area (A) of a square is given by the square of the side length (a):
$A = a^2$

Substitute the value of the side length into the equation to find the area of the square $A =8$ So, the area of the square is8 square units. The correct answer is C.8.