Question

Find the area of the shaded region if ABCD is a square

Answer 1

 shaded area  = area of ΔABE + area of ΔCDE
 = 16*4*1/2 + 16*12*1/2
= 16*16/2 = 128cm²

Answer 2

Length of side of the given square = 4+12 = 16cm .

Now Area of Unshaded triangles is composed of two right triangles .


Area of unshaded portion = 1/2(8)(16)+1/2(16)(8) = 64+64 = 128 cm²

Area of total figure = 16² = 256 cm² .

Hence,Area of shaded portion= Area of Square - Area of unshaded region = 256-128=128cm² .

Or Area of shaded portion = Area of ΔABE+ ΔEDC = 1/2(4)(16)+1/2(12)(16)=32+96=128cm²