Question

Find the area enclosed by the given figure ABCDEF as per dimensions given herewith.

Answer 1

Given: A figure ABCDEF 

AB = 20 cm 

BC = 20 cm 

ED = 6 cm 

AF = 20 cm 

AB || FC 

FC = 20 cm 

Let distance between FC and ED be h = 8 cm 

FC || ED 

Here, 

From the figure we can see that ABCF forms a square and EFCD forms a trapezium. 

Area of square = (side length)² 

Area of trapezium = \(\frac{1}{2}\)× (sum of parallel sides) × height

Therefore, 

Area of the figure ABCDEF = Area of square (ABCF) + Area of trapezium (EFCD) 

Here, 

Area of square (ABCF) = (AB)² = (20)² = 400 cm² 

Area of trapezium (EFCD) = \(\frac{1}{2}\)× (FC + ED) × h = \(\frac{1}{2}\)× (6 + 20) × 8 = 104 cm 2

∴ Area (ABCDEF) = Area of square (ABCF) + Area of trapezium (EFCD)= 400 + 104 = 504 cm².

∴ Area (Fig. ABCDEF) = 504 cm².