Is the area of the flower the same in the front and back view? Justify your answer with proper working. (Take ? = 22/7)

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Solution

Q.
Pragati made a paper flower using 4 identical circles and a dotted square. The front view and back view of the flower is as shown below.

The diameter of each circle is the same as the length of the side of the square, 42 m.

Based on the above information, answer the following questions:

(iii) (a) Is the area of the flower the same in the front and back view Justify your answer with proper working. $(T a k e π = 22 / 7)$

1 View are equal

2 View are not equal

3 none of these

4 Only Front

Ans.
(1)

We have,

Area of the flower from front view

=Area of the four circles + Area of dotted region

$= 4 \times π r^{2} + 378 = 4 \times \frac{22}{7} \times (21)^{2} + 378 = \frac{88}{7} \times 21 \times 21 + 378 = 5544 + 378 = 5922 m^{2}$

$A r e a o f t h e f l o w e r f r o m b a c k v i e w$

$= 4 \times \frac{3}{4} \times Area of a circle + Area of a square = 3 \times {πr}^{2} + (42)^{2}$

$= 3 \times \frac{22}{7} \times 21 \times 21 + 1764 = 4158 + 1764 = 5922 m^{2}$

$Yes, area of the flower from front view and back view are equal .$

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