Question

In the figure ABCD and BEFG are two squares with side lengths 4 cm and 10 cm respectively. The area of the shaded region (in cm2) is
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Answer 1

Answer:

Step-by-step explanation:

Lel angle FAE = X

tan X = FE/AE = PB/AB

             10/14 = PB/4

               PB = 20/7

area of ABPA = (1/2)xABxPB

                      = 0.5x4x20/7

                       =5.71 cm2

Answer 2

Given : ABCD and BEFG are two squares with side lengths 4 cm and 10 cm respectively

To Find : The area of the shaded region (in cm²)

Solution:

ABCD & BEFG are square

=> ∠B  = ∠E = 90°

∠BAP = ∠EAF  ( common)

=> Δ ABP ≈ Δ AEF

=> AB/ AE =  BP/EF

AB = 4  cm

AE = AB + BE = 4 + 10  = 14  cm

EF = 10  cm

=> 4/14 = BP/10

=> BP = 40/14  = 20/7 cm

Area of shaded region = (1/2) * AB  * BP

= (1/2) 4 * 20/7

= 40/7

=  5.714  cm²

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