Class 8 Maths Mensuration Area of Polygon

Area of Polygon

We split a polygon into triangles and then find its area. Ex: To find the area of given figure, by constructing two diagonals AC and AD

the pentagon ABCDE is divided into three parts.

So, area ABCDE = area of Δ ABC + area of Δ ACD + area of Δ AED.

Problem: 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:

Given: Octagon having eight equal sides, each 5 m.

Construction: Divided the octagon in 3 figures, two trapeziums whose parallel and perpendicular sides are 11 m and 4 m respectively and third figure is rectangle having length and breadth 11 m and 5 m  respectively. Now Area of two trapeziums = 2 * 1/2 * (a + b) * h

= 2 * 1/2 * (11 + 5) * 4

= 16 * 4 = 64 m2

And Area of rectangle = length * breadth

= 11 * 5 = 55 m2

Hence, total area of octagon = 64 + 55 = 119 m2

Solid Shapes

Many objects that we see in our day to day life like book, pencil box, ice cream cone, football and cylinder are three-dimensional objects (solid shapes). All these objects occupy some shape and have three dimensions- length, breadth and height or depth.

Some shapes have two or more than two identical (congruent) faces. For example the cylinder has congruent circular faces that are parallel to each other.

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