Question

Find the area of the shaded region

Answer 1

Answer:

(a) 2,450 $m^{2}$

(b) 120

(c) 474.25 $m^{2}$

(d) 1,050 $m^{2}$

(e) 20

(f) 180

Step-by-step explanation:

Area of the shaded region:

(a)

Required Area = Area of the rectangle - 5 times Area of each square

= (58x45 - 5x8x8) $m^{2}$ = 10(29x9 - 2x8) $m^{2}$ = 10(261 - 16) $m^{2}$ = 2,450 $m^{2}$

(b) Required Area = Area of the rectangle [12x(3+3+3+3+3)] - 2 times Area of rectangle (8x3) - Area of rectangle [(8-4)x3] = 12x15 - 2x24 - 4x3 = 180-48-12=120

(c) Required Area = Area of the rectangle [86.5x52.5] $m^{2}$ - 4 times Area of rectangle [$\frac{86.5-3.5}{2}$x$\frac{52.5-3.5}{2}$] $m^{2}$ = (4541.25 - 83x49) $m^{2}$ =474.25 $m^{2}$

(d) Required Area = Area of the rectangle [40x75] $m^{2}$ - Area of rectangle [30x65] $m^{2}$ = 10x5(60 - 39) $m^{2}$ = 10x5x21 $m^{2}$ = 1,050 $m^{2}$

(e) Required Area = ($\frac{1}{2}$ of 8x3 + $\frac{1}{2}$ of 8x2) = 20

(f) Required Area = Area of rectangle (12x30) - Area of Triangle ($\frac{1}{2}$ of 12x12) - Area of Triangle ($\frac{1}{2}$ of 12x18) = 12x30 - 6x12 - 9x12 = 12(30 - 6 - 9) = 12x15 = 180