"Question 9 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 Mensuration Page 178"
Answers
Mensuration:
Mensuration is the branch of mathematics which concerns itself with the measurement of Lengths, areas & volume of different geometrical shapes or figures.
Plane Figure: A figure which lies in a plane is called a plane figure.
For e.g: a rectangle, square, a rhombus, a parallelogram, a trapezium.
Perimeter:
The perimeter of a closed plane figure is the total length of its boundary.
In case of a triangle or a polygon the perimeter is the sum of the length of its sides.
Unit of perimeter is a centimetre (cm), metre(m) kilometre(km) e.t.c
Area: The area of the plane figure is the measure of the surface enclose by its boundary.
The area of a triangle are a polygon is the measure of the surface enclosed by its sides.
A square centimetre (cm²) is generally taken at the standard unit of an area. We use square metre (m²) also for the units of area.
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Solution;
Figure is in the attachment...
Given:
Sides of octagon= 5 m.
Construction: We Divide the octagon in 3 figures, two are trapeziums whose parallel and perpendicular sides are 11 m and 5 m respectively and third figure in middle is rectangle having length and breadth 11 m and 5 m.
Area of Trapezium
= (1/2) × (Sum of parallel sides) × Perpendicular distance
= (1/2) (11+5)4
= 16 x 2
= 32m²
Area of 2 trapeziums = 64 m²
Area of Rectangle = Length x Breadth
= 11 x 5 = 55
Area of Rectangle = 55 m²
Total area of octagon = 64 + 55= 119
Total area of octagon = 119 m²
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Hope this will help you...
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