Question

Find the area of shaded portion . Please give step by step explanation.​

Answer 1

Answer:

A) 30,23 cm2

B) 503,72 cm2

Step-by-step explanation:

A) The area of shaded portion equals (the area of the rectangle) - (the area of the semi-circle).

Ar- area of the rectangle

Asc - area of the semi-circle

Ax- area of the shaded portion

________________________

Ar = (7 * 10,5) $cm^{2}$ = 73,5 cm2

Asc = ($r^{2}$π)/2 = (5,25 cm * 5,25 cm * 3,14) / 2 = 43,27 cm2

*** note that r=(10,5/2) cm = 5,25 cm and the approximate value of π=3,14 ***

Ax = Ar - Asc

Ax = 73,5 cm2 - 43,27 cm2

Ax = 30,23 cm2

B) The area of shaded portion equals (the area of the square) + (the area of the 4 equal semi-circles or 2 full circles)

As - area of the square

Asc - area of 1 semi-circle

Ax - area of the shaded portion

___________________________

As = 14 * 14 = 196 cm2

Asc = (7 * 7 * 3,14) / 2 = 76,93 cm2

Ax = As + 4 * Asc = (196 + 4* 76,93) cm2 = 503,72 cm2