Question

32) Find the area of the given composite shape :
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Answer 1

Step-by-step explanation:

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Answer 2

ANSWER

Approach:

• We will divide the given figure into 3 parts, and then add the area of each of them.

Solution:

We will take the given hexagon as a regular one, i.e. with all it’s sides equal(=5m)

(Refer the attachment for the division of the given hexagon.)

So, Part I and Part II are trapezia(plural of trapezium) and Part III is a rectangle.

Dimensions of Part I and Part II:

⇒ Height = 4m; Length of one side = 5m; Length of other side = 11m

Dimensions of Part III:

⇒ Length = 11m; Breadth = 5m

So,

⇒ Area of Part I = Area of Part II

⇒ Area of trapezium = ¹/₂ * (Sum of parallel sides) * height

⇒ Area of Part I = ¹/₂ * (5+11) * 4

⇒ Area of Part I = 2 * 16

⇒ Area of Part I = 32m² = Area of Part II

And,

⇒ Area of rectangle = length * breadth

⇒ Area of Part III = 11 * 5

⇒ Area of Part III = 55m²

Hence,

⇒ Area of complete figure = Area of Part I + Area of Part II + Area of Part III

⇒ Area of complete figure = 32m² + 32m² + 55m²

⇒ Area of complete figure = 119m²

Formulae Used:

• Area of trapezium = ¹/₂ * (Sum of parallel sides) * height
• Area of rectangle = length * breadth