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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