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# Diagram of the adjacent picture frame has outer dimensions = 24 cm × 28 cm and inner dimensions 16 cm × 20 cm. Find the area of each section of the frame, if the width of each section is same.

**Solution:**

Visually, there are four trapeziums and one rectangle in the given figure as shown below.

Given that the width of each section is same.

Therefore, IB = BJ = CK = CL = DM = DN = AP = AO ..... (1)

IL = IB + BC + CL

28 = IB + 20 + CL

28 − 20 = IB + CL

8 = IB + CL

But, IB = CL [From equation (1)]

Thus, 2IB = 8

IB = 4 cm

Hence IB = BJ = CK = CL = DM = DN = AP = AO = 4 cm

We know that, ABEH, CDGF, BEFC and ADGH are all trapezium

Area of trapezium ABEH = Area of trapezium CDGF [By symmetry]

= 1/2 × (AB + HE) × IB

= 1/2 (16 + 24) × 4 = 80 cm²

Area of trapezium BEFC = Area of trapezium ADGH [By symmetry]

= 1/2 × (BC + EF) × BJ

=1/2 × (20 + 28) × 4 = 96 cm²

Area of rectangle ABCD = BC × DC

= 20 cm × 16 cm = 320 m²

Thus, the area of section ABEH and CDGF is 80 m², the area of section BEFC and ADGH is 96 m² and the area of section ABCD is 320 m².

**☛ Check: **NCERT Solutions for Class 8 Maths Chapter 11

**Video Solution:**

## Diagram of the adjacent picture frame has outer dimensions = 24 cm × 28 cm and inner dimensions 16 cm × 20 cm. Find the area of each section of the frame, if the width of each section is same

Class 8 Maths NCERT Solutions Chapter 11 Exercise 11.2 Question 11

**Summary:**

Diagram of the adjacent picture frame has outer dimensions = 24 cm × 28 cm and inner dimensions 16 cm × 20 cm. The area of each section of the frame, if the width of each section is same are as follows: the area of section ABEH and CDGF is 80 m², the area of section BEFC and ADGH is 96 m² and the area of section ABCD is 320 m².

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