Find area and perimeter of shaded regions below

Mathematics

1 answer:

aleksandrvk [35]3 years ago

6 0

Answer:

Step-by-step explanation:

ABCD is a square.

side = 24 cm

Area of square = side * side = 24 * 24 = 576 cm²

Semicircle:

d = 24 cm

r = 24/2 = 12 cm

Area of semi circle =πr²

= 3.14 * 12 * 12

= 452.16 cm²

Area of shaded region = area of square - area of semicircle + area of semicircle

= 576 - 452.16 + 452.16

= 576 cm²

Perimeter:

Circumference of semicircle = 2πr

= 2 * 3.14 * 12

= 75.36

Perimeter = 2* circumference of semicircle + 24 + 24

= 2 * 75.36 + 24 + 24

= 150.72 + 24 + 24

= 198.72 cm

You might be interested in

Pythagoras help needed please

boyakko [2]

Answer:

See explanation

Step-by-step explanation:

Find the diagonal of the square. The side of the square is 5 cm long. By the Pythagorean theorem,

$\text{Diagonal}^2=\text{Side}^2+\text{Side}^2\\ \\\text{Diagonal}^2=5^2+5^2\\ \\\text{Diagonal}^2=25+25\\ \\\text{Diagonal}^2=50\\ \\\text{Diagonal}=\sqrt{50}=5\sqrt{2}\approx 7.07\ cm$

If the square (being inside the circle) touches the circle, then the diagonal of the square is exactly the diameter of the circle. The diameter of the circle is twice the radius of the circle, so

$\text{Diameter}=2\times 5=10\ cm$