Question

Can you please solve this for me asap?​

Answer 1

Hi there! :)

Answer:

(a) ≈ 3.61 cm.

(b) = 2.77 cm².

Use the Pythagorean theorem to solve for the side-length of DC. Let "s" represent the side-lengths:

s² + s² = 26

2s² = 26

Divide both sides by 2 to simplify:

s² = 13

Take the square root of both sides:

s = √13 ≈ 3.61 cm.

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Calculate the shaded region by subtracting the area of the arc from the area of the square. DC represents the radius of the circle that the arc is apart of. Therefore:

Area of arc AC = 1/4 (πr²)

Solve for the area:

AC = 1/4 (π · (3.61)²)

AC = 1/4 (40.92)

AC = 10.23 cm²

Subtract this area from the area of the square (A = s²)

A = (√13)²

A = 13 cm²

13 - 10.23 = 2.77 cm²

Therefore, the solutions are:

(a) ≈ 3.61 cm.

(b) = 2.77 cm².