Question

In the adjoining fig,ABC is a right angled triangle at B.A semicircle is drawn on AB as diameter.If AB=12 cm,BC=5 cm,find the perimeter of the shaded region.​

Answer 1

Option (c)

Solution :-

From the given figure,

∆ABC is a right angles triangle

right angle at B.

AB is the diameter

AB = 12 cm

BC = 5 cm

We know that

Area of a triangle = (1/2)×bh sq units

Area of ∆ABC = (1/2)×AB× BC

=> Area of ∆ ABC = (1/2)×12×5 cm²

=>Area of ∆ ABC = 6×5 cm²

Area of ∆ ABC = 30 cm²

And

Diameter = 12 cm

Radius = Diameter/2

= AB /2

= 12/2

Radius of the semi circle= 6 cm

We know that

Area of a semi circle = πr²/2 sq.units

Area of the semi circle = π×6²/2 cm²

=> Area of the semi circle = π×6×6×2 cm²

=> Area of the semi circle = π×6×3 cm²

Area of the semi circle = 18π cm²

Now,

Area of the shaded region

Area of the shaded region= Area of ∆ ABC + Area of the semi circle

= 30+18π cm²

Answer :-

Area of the shaded region is

(30+18π) cm²

Used formulae:-

• Area of a triangle = (1/2)×bh sq units

• b = base
• h = height or altitude

• Area of a semi circle = πr²/2 sq.units

• r = radius
• π = 22/7
• d = 2r
• r = d/2
• d = diameter

Answer 2

QUESTION :-

In the adjoining fig,ABC is a right angled triangle at B.A semicircle is drawn on AB as diameter.If AB=12 cm,BC=5 cm,find the perimeter of the shaded region

GIVEN :-

AB = 12 cm

BC = 5 cm

<B = 90°

TO FIND :-

area of shaded region = ?

SOLUTION :-

area of semicircle + area of ∆ABC

area of semicircle = πr² / 2 = π(6)²/2 = 18 π ²

area of ∆ABC = 1/2 × AB ×BC

= 1/2 × 12 × 5 = 30 cm²

Total area = (30+ 18π) cm²

Answer: Hence the area of shaded region

is (30+18 π) cm² So correct option is C