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Q.

Find the area of a figure formed by a square of side 8 cm   and an isosceles triangle with base as one side of the square and perimeter as 18 cm  .


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a

56c m 2  

b

66c m 2  

c

76c m 2  

d

86c m 2   

answer is C.

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Detailed Solution

Given a square of side 8 cm and isosceles triangle with perimeter 18 cm.
Assume, equal side of the isosceles triangle = x.
As, the base of isosceles triangle is on a square of side 8 cm, therefore, base = 8 cm.
Perimeter of square is sum of all sides.
The perimeter is,
⇒x+x+8=18  
⇒2x+8=18  
⇒2x=18−8  
⇒2x=10  
⇒x= 10 2  
⇒x=5  
Height of the triangle is,
h= side 2 − base 2 ⇒h= 5 2 − 4 2  
⇒h= 25−16  
⇒h= 9  
⇒h=3  
The area of the figure formed is,
A= 1 2 ×base×height+sid e 2 ⇒A= 1 2 ×8×3+ 8 2  
⇒A=4×3+64  
⇒A=12+64  
⇒A=76c m 2  
Therefore, the area is 76c m 2  .
Hence, option 3 is correct.
 
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