Top surface of a raised platform is in the shape of a regular octagon as shown in the figure. Find the area of the octagonal surface
Solution:
Visually, the area of the octagonal surface will be the sum of the area of two trapezia and the area of rectangular region.
Area of octagon ABCDEFGH = Area of trapezium ABCH + Area of rectangle HCDG + Area of trapezium EFGD
Side of the regular octagon = 5 cm
Area of trapezium ABCH = Area of trapezium EFGD
Area of trapezium ABCH = 1/2 × (AB + CH) × AI
= 1/2 × (5 m + 11 m) × 4 m
= 1/2 × 16 m × 4 m
= 32 m²
Area of trapezium ABCH = Area of trapezium EFGD = 32 m²
Area of rectangle HCDG = HC × CD = 11 m × 5 m = 55 m²
Area of ABCDEFGH = Area of trapezium ABCH + Area of rectangle HCDG + Area of trapezium EFGD
= 32 m²+ 55 m²+ 32 m²
= 119 m²
Thus the area of the octagonal surface is 119 m²
☛ Check: NCERT Solutions for Class 8 Maths Chapter 11
Video Solution:
Top surface of a raised platform is in the shape of a regular octagon as shown in the figure. Find the area of the octagonal surface
Class 8 Maths NCERT Solutions Chapter 11 Exercise 11.2 Question 9
Summary:
Top surface of a raised platform is in the shape of a regular octagon as shown in the figure. The area of the octagonal surface is 119 m².
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