Question

find the area of the shaded region in which the dimension given
is in centimetre ​

Answer 1

Answer- The above question is from the chapter 'Area and Perimeter'.

Concept used: Area of Triangle = 1/2 × Base × Perpendicular

Question: Find the area of the shaded region in which the dimension given

is in centimetre. (Pic has been attached.)

Solution: Area of shaded region = Area of big Δ - Area of small Δ

Area of big Δ

Perpendicular = 8 cm

Base = 15 cm

Area of big Δ = 1/2 × Base × Perpendicular

                       = 1/2 × 8 × 15 = 4 × 15 = 60 cm²

Area of small Δ

Perpendicular = 4 cm

Base = ?

For finding the base, we will use Pythagoras Theorem in the big Δ.

i.e. AB² + AC² = BC²

8² + 15² = BC²

BC² = 64 + 225

BC² = 289

BC = √289

BC = 17 cm

Base = 17 cm

Area of small Δ = 1/2 × Base × Perpendicular

                           = 1/2 × 17 × 4 = 17 × 2 = 34 cm²

∴ Area of shaded region = Area of big Δ - Area of small Δ

                                           = 60 - 34    

                                           = 26 cm²

∴ Area of shaded region of Δ = 26 cm².