Question

The diagram shows a circle inside a square.

D
C
28
ABCD is a square of side 10 cm.
Each side of the square is a tangent to the circle.
10 cm
Work out the total area of the shaded regions in terms of TT.
Give your answer in its simplest form.
B
Diagram NOT
accurately drawn
er) & siprislostjo

Answer 1

The total area of the shaded regions within the square, which is 100 cm² minus the area of the inscribed circle, 25π cm², is 100 - 25π cm².

Step-by-step explanation:

To find the total area of the shaded regions within the square, we must calculate the area of the square and then subtract the area of the circle.

The area of the square is given by the formula Area of square = side × side, so with a side of 10 cm, the area is 100 cm².

The side of the square is also the diameter of the circle, so the radius (r) of the circle is half of the side of the square, which is 5 cm. The area of the circle is calculated using the formula Area of circle = πr².

Since the radius (r) is 5 cm, the area of the circle is π × (5 cm)² = 25π cm². To find the area of the shaded region, we subtract the area of the circle from the area of the square.

Therefore, the total area of the shaded regions is 100 cm² - 25π cm². This simplifies to 100 - 25π cm².

Answer 2

100 - 25π cm²

Step-by-step explanation:

Area of Square = 10 × 10 = 100 cm²

Area of Circle = πr² = r² × π = 25π cm²

Area of Shaded Regions = 100 - 25π cm²