Question

04
The diagram shows a window made up of a large semicircle and a rectangle
The large semicircle has 4 identical sections, A, B, C, D, and a small semicircle, E
The rectangle has three identical square sections, F, G and H.
The side of each square is 20 cm.


Find an expression, in the form a+b pi,for
(a) the area of the whole window
13
(b) the perimeter of section

Answer 1

Solution :-

a) The area of the whole window = Area of 3 squares F,G and H + Area of 4 identical sections, A, B, C, D, and a small semicircle, E .

→ Area of window = Area of rectangle made with 3 squares of length 20*3 cm and breadth as 20 cm + Area of half semi circle made with 4 identical sections and small semi circle whose diameter is equal to 60 cm .

so,

→ Area of window = L * B + (1/2)πr²

→ Area of window = 60 * 20 + (1/2)π(60/2)²

→ Area of window = (1200 + 450π) cm² (Ans.)

b) The perimeter of section B = 2(Large semi - circle radius - small semi - circle radius) + (1/4) of perimeter of large semi - circle + (1/4) of perimeter of small semi - circle

→ Perimeter of section B = 2(30 - 10) + (1/4)[(1/2)2πR + (1/2)2πr]

→ Perimeter of section B = 2 * 20 + (1/4)[πR + πr]

→ Perimeter of section B = 40 + (1/4)[30π + 10π]

→ perimeter of section B = 40 + (1/4)40π

→ perimeter of section B = (40 + 10π) cm (Ans.)

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