## Book: RS Aggarwal - Mathematics

### Chapter: 18. Area of Circle, Sector and Segment

#### Subject: Maths - Class 10th

##### Q. No. 53 of Exercise 18B

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53
##### A child draws the figure of an aeroplane as shown. Here, the wings ABCD and FGHI are parallelograms, the tail DEF is an isosceles triangle, the cockpit CKI is a semicircle and CDFI is a square. In the given figure, BP ⊥ CD, HQ ⊥ FI and EL ⊥ DF. If CD = 8 cm, BP = HQ = 4 cm and DE = EF = 5 cm, find the area of the whole figure. [Take π = 3.14.]

Area of whole figure = ar || ABCD + ar || FGHI + ar DCIF + ar DEF + area semicircle

CD = 8 cm, BP = HQ = 4 cm, DE = EF = 5 cm, CI = 8 cm

ar ABCD = ar FGHI = base × height

ar ABCD = ar FGHI = BP×DC

ar ABCD = ar FGHI = 4×8

ar ABCD = ar FGHI = 32 cm2 eqn1 and eqn2

ar DCIF = area of square = side×side

ar DCIF = DC×CI

ar DCIF = 8×8

ar DCIF = 64 cm2 eqn3

Consider ∆DEF, EFDF and ∆DEF is isosceles

So, FL = LD

FL = LD = 4 cm

In ∆DEL, DLE = 90°

52 = EL2 + 42 (putting the values)

25 = EL2 + 16

25 – 16 = EL2

EL2 = 9

EL = 3 cm

Area of ∆DEF = 4×3

Area of ∆DEF = 12 cm2 eqn4

R = 4 cm

Area of semicircle = 3.14×8

Area of semicircle = 25.12 cm2 eqn5

Area of whole figure = eqn1 + eqn2 + eqn3 + eqn4 + eqn5

Area of whole figure = 32 + 32 + 64 + 12 + 25.12

Area of whole figure = 165.12 cm2

Area of the whole figure is 165.12 cm 2.

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