Question

★★TRICKY QUESTION★★

In the given figure, ABCD is a Square, and, CDEF is a Rhombus.

If,
Area of square = 625cm^2
Area of Rhombus = 500cm^2

Find the area of shaded region.

Explanation required.

Answer 1

 Hi Dear :) 

ABCD is a square 

CDEF is a rhombus 

Area of square = 625 cm²

Area of rhombus = 500 cm²

Now Look at BC and EF where they intersect take that point R 

Here DCRE is a trapezium 

we can get area of shaded region by subtracting area of trapezium DCRE from Area of square ABCD 

Now, 

side of square = √625 = 25 cm 

area of rhombus = b x h 

500 =  25 x h 

we take base of rhombus as 25 because base of rhombus = side of square = DC

Now , 

h = 500  /25 

h = 20 cm 

using trigonometry in ECR 

ER/h = sin45 

ER = 20/√2

Area if trapezium DCRE 

1/2 ( 25 + 20/√2 ) x 20 

250 + 200/√2

250 + 141.84

391.84 cm²

Area of shaded region = 625 - 391.84 = 233.15 ≈ 233.2 cm²