Question

The figure shows a rhombus and two trapeziums. Find the total area of the figure. (All measurements shown are in cm.)

(1) 400 (2) 394 (3) 198 (4) 294

FIGURE IS SHOWN IN THE ATTACHMENT.
Please Check........

Answer 1

Area of trapezium=1/2 x (sum of parallel sides) x height
1/2 x (16+10) x 6=1/2 x 16 x 6=78 sq.cm
In the case of rhombus the area is 1/2 x diagonal₁ x diagonal₂
But in the figure the second diagonal is not give so we have to find it  out.
We know that the diagonals of a rhombus bisect each other at right angle.
First we have to bisect the diagonal which has length of 16cm into 8 cm.
By using Pythagoras theorem
H²=P²+B²
10²=8²+B²
100=64+B²
100-64=B²
36=B²
6=B
THEREFORE SECOND DIAGONAL=2B=2 X 6=12CM
area of rhombus=1/2*16*12=96cm²
area of trapezium₂=1/2*(10+20)*8
1/2*30*8=120cm²
Area of the figure=(120+96+78)=294cm₂
So the answer is (4) 294cm²