Question

7. The given figure
shows a right-
angled triangle ABC
and an equilateral
triangle BCD.
Find the area of
the shaded portion.
-
8 cm
-
​

Answer 1

Heya!

REQUIRED AREA ( Area ABD ) = AREA OF ∆ ABC - AREA OF ∆ DBC

=>

Area of ∆ ABC = 1/2 ( 8 × AB )

(16)² = AB² + 8²

AB = √(192)

AB= 8√3cm

So,

Area of ∆ ABC = 1/2( 8 × 8√3 ) = 32√3cm²

=>

Area of ∆ DBC = 8²√3/4

Becoz area of equilateral ∆ having sides a is given by a²√3/4

Area of ∆ DBC = 16√3cm².

So, REQUIRED AREA= (32√3 - 16√3)cm²

Area of ∆ ABD = 16√3cm²