Question

In the given figure, ABCD is a trapezium with AB || DC, AB = 18 cm DC = 32 cm and the distance between AB and DC is 14 cm. Circles of equal radii 7 cm with centres A, B, C and D have been drawn. Then find the area of the shaded region.(Use $(\pi=\frac{22}{7})$ )​

Answer 1

Answer:

The Area of shaded region is 196 cm².

Step-by-step explanation:

Given :  

AB = 18 cm , DC = 32 cm , Distance between AB  and DC (h) = 14 cm & radius of each circle (r) = 7cm

Since , AB ||DC  

Therefore , ∠A + ∠D = 180° & ∠B + ∠C = 180°  

[CO INTERIOR ANGLES are supplementary]

Area of sector =  (θ /360) ×πr²

Area of sector with ∠A & ∠D = (180 /360) × 22/7 × 7²  

= ½ × 22 × 7 = 11 × 7

Area of sector with ∠A & ∠D = 77 cm²

Similarly,  Area of sector with ∠B & ∠C = (180 /360) × 22/7 × 7²  

= ½ × 22 × 7 = 11 × 7

Area of sector with ∠B & ∠C  = 77 cm²

Area of trapezium = ½ (sum of parallel sides) ×distance between Parallel sides(h)

Area of trapezium = ½ (AB + DC ) ×(h)

Area of trapezium = ½(18 + 32) × 14

= ½ (50) × 14  

= 25 × 14  

= 350 cm².

Area of trapezium = 350 cm².

Area of shaded region = Area of trapezium - (Area of sector with ∠A & ∠D + Area of sector with ∠B & ∠C)

= 350 -(77 + 77)

= 350 - 154

= 196 cm²

Area of shaded region = 196 cm²

Hence, the Area of shaded region is 196 cm².

HOPE THIS ANSWER WILL HELP YOU….

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