Question

Calculate the area of shaded triangle.​

Answer 1

Required Answer:-

Given To Find:

• The area of the shaded region.

Solution:

Given that, (See the image)

→ OD = 3cm

→ OC = 6cm

Therefore,

→ CD = OD + OC

→ CD = 3cm + 6cm

→ CD = 9cm

→ ABCD is a rectangle.

→ AB = CD

→ AB = 9cm

→ Area of ABCD = AB × BC

→ Area of ABCD = 9 × 7 cm²

→ Area of ABCD = 63cm²

Area of ∆DOP,

= 1/2 × PD × OD

= 1/2 × 4 × 3 cm²

= 6cm²

→ Area of ∆DOP = 6cm²

Area of ∆BOC,

= 1/2 × OC × BC

= 1/2 × 6 × 7 cm²

= 21cm²

→ Area of ∆BOC = 21cm²

Area of ∆ABP,

= 1/2 × AB × AP

= 1/2 × CD × AP (∵ AB = CD)

= 1/2 × CD × (AD - PD)

= 1/2 × 9 × (7 - 4)

= 1/2 × 27

= 13.5cm²

→ Area of ∆ABP = 13.5cm²

Therefore, area of shaded region,

= Area of rectangle - Area of three triangles

= 63 - (6 + 21 + 13.5) cm²

= 63 - 40.5cm²

= 22.5cm²

→ So, the area of the shaded region is 22.5cm²

Note the formula used:

• Area of a rectangle = Length × Breadth.
• Area of a triangle = 1/2 × Base × Height.

Answer:

• The area of the shaded region is 22.5cm²

•••♪