Question

Math step by step answer

Answer 1

1) 165.7 cm²

2) 736 cm²

3) 155.5 cm²

4) 169 cm²

Explanation:

1) To find the area of shaded region, subtract the area of circle from the area of triangle.

r = 4 cm

`\boxed{\text{\bf Area of circle = $\pi r^2$}}`

`= 3.14 * 4 * 4 \\\\= 50.27 \ cm^2`

Triangle :

base = b = 18 cm

height = h = 24 cm

`\boxed{\text{\bf Area of triangle = $(1)/(2)b*h$}}`

`= (1)/(2)*18*24\\\\= 9 * 24\\\\= 216 \ cm^2`

Area of shaded part = area of triangle - area of circle

= 216 - 50.27

= 165.73

= 165.7 cm²

3) To find the area of shaded part, subtract the area of semicircle from the area of square.

side = 16 cm

`\boxed{\text{\bf Area of square = side * side}}`

`= 16 * 16\\\\= 256 cm^2`

diameter of semicircle = side of the square

d = 16 cm

r = 16÷ 2

r = 8 cm

`\boxed{\text{\bf area of semicircle = $(1)/(2)\pi r^2$}}`

`= (1)/(2)*3.14*8*8\\\\= 100.53 \ cm^2`

Area of shaded part = area of square - area of semicircle

= 256 - 100.53

= 155.47

= 155.5 cm²

2) To find the area of shaded part, add the area of rectangle I and the area of rectangle II.

Rectangle I:

l = 32 - 8 = 24 cm

w = 24 cm

So, it is a square.

Area of rectangle I = 24 * 24

= 576 cm²

Rectangle II:

l = 8 cm

w = 24 - 4 = 20 cm

Area of rectangle II = 8 * 20

= 160 cm²

Area of shaded part = area of rectangle I + area of rectangle 2

= 576 + 160

= 736 cm²

4) length = l = 26 cm

width = w = 13 cm

Rectangle can be divided into two congruent triangles through its diagonal. So, the area of shaded part can be found by dividing the area of rectangle by 2.

Area of rectangle = l * w

= 26 * 13

= 338 cm²

Area of shaded part = area of rectangle ÷ 2

= 338 ÷ 2

= 169 cm²