Page 256 - Start Up Mathematics_7

POLYGON PUZZLE
C
In the given figure, each small square of the grid A B
has an area of 1 square unit. Answer the following
questions:
(a) Name each of the following polygons from D E F
A to K.

(b) Find the area of each polygon.
(c) What is the area of the entire figure? I
(d) Which polygons have equal area? H

(e) Which figure is formed by combining G J
polygons A and B? Find its area in two K
different ways. L

At a Glance

1. Perimeter is the length of the boundary of any closed plane figure.
2. Area is the surface or region enclosed inside a closed boundary.

3. (a) Perimeter of a rectangle = 2 × (length + breadth)
(b) Perimeter of a square = 4 × side
(c) Area of a rectangle = length × breadth

(d) Area of a square = side × side
4. (a) Area of a parallelogram = base × altitude
1
(b) Area of a triangle = (area of parallelogram formed by duplicating the triangle)
2
1
= × base × height
2
5. (a) Circumference of a circle is the length of the boundary of the circle.
∴ circumference = 2πr = π × d
(b) Area of a circle = πr 2
6. (a) Area between two rectangles h cm b
= Area of outer rectangle – area of inner rectangle

= ab – (a – 2h)(b – 2h) a
(b) Area between two concentric circles

= Area of outer circle – area of inner circle r
2
= πR – πr 2 R
1
7. Area of trapezium = (sum of parallel sides) × h h 1
2
1 d
8. Area of rhombus = (product of diagonals)
2 h 2
1
= × d × d
2 1 2

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