Question

find the area of the shaded portion​

Answer 1

Given:-

• DC = 11 cm
• BC = 14 cm
• EG = 5 cm
• HF = 4 cm
• ∠GEB = ∠HFC = 90°

To find:-

• Area of the shaded region.

Answer:-

For □ABCD:

Area of rectangle ABCD = BC * DC

= 14 cm * 11 cm

= 154 cm²

For △AGB:

As GE is the altitude/height, we can say that,

Area of △AGB = (1/2) * AB * GE

And as ABCD is a rectangle, AB = DC = 11 cm

So, area of △AGB = (1/2) * (11 cm) * (5 cm)

= 55/2 cm²

= 27.5 cm²

For △DHC:

As HF is altitude/height, we can say that,

Area of △DHC = (1/2) * DC * HF

= (1/2) * (11 cm) * (4 cm)

= 44/2 cm²

= 22 cm²

We observe that,

area of shaded region = Area of □ABCD - (Area of △AGB + Area of △DHC)

= 154 cm² - (27.5 cm² + 22 cm²)

= 154 cm² - 49.5 cm²

= 104.5 cm² Ans.