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Long Answer Type

1. (a) Match the following figures with their respective areas in the box.

(b) Write the perimeter of each shape.

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A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area?

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Mrs. Kaushik has a square plot with the measurement as shown in the figure. She wants to construct a house in the middle of the plot. A garden is developed around the house. Find the total cost of developing a garden around the house at the rate of Rs 55 per m².

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4.
The shape of a garden is rectangular in the middle and semi-circular at the ends as shown in the diagram. Find the area and the perimeter of this garden. [Length of rectangle is 20 - (3.5 + 3.5) meters.]

For the semi-circular part:
Diameter of the semi-circle = 7 m
∴ Radius of the semi-circle =

7 over 2 equals 3.5 space straight m

Area of the 2 semi-circles =

space space space space 2 open square brackets 1 half πr squared close square brackets

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equals 22 over 7 cross times 35 over 10 cross times 35 over 10 space straight m squared

equals space fraction numerator 11 cross times 35 over denominator 10 end fraction straight m squared space equals space 38.5 space straight m squared

Also, perimeter of the 2 semicircles =

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equals space 2 cross times 22 over 7 cross times 35 over 10 space straight m

= 22 m
For rectangular part:
Length of the rectangle = 20 - (3.5 + 3.5) m
= 13 m
Breadth of the rectangle = 7 m
∴ Area = Length x Breadth
= 13 m x 7 m
= 91 m²
Perimeter = 2 x [Length + Breadth]
= 2 x [13 m + 0 m]
= 2 x 13 m
= 26 m
Now, Area of the garden = (38.5 + 91)m²
= 129.5 m²
Perimeter of the garden = 22 m + 26 m
= 48 m

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Short Answer Type

A flooring tile has the shape of a parallelogram whose base is 24 cm and the corresponding height is 10 cm. How many such tiles area required to cover a floor of area 1080 m²?
(If required you can split the tiles in whatever way want to fill up the corners.)

2124 Views

Long Answer Type

An ant is moving around a few food pieces of different shapes scattered on the floor. For which food-piece would the ant have to take a longer round? Remember, circumference of a circle can be obtained by using the expression $straight c equals 2 πr comma$ where r is the radius of the circle.

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Short Answer Type

7. Nazma’s sister also has a trapezium shaped plot. Divide it into three parts as shown. Show that the area of trapezium WXYZ =

straight h fraction numerator left parenthesis straight a plus straight b right parenthesis over denominator 2 end fraction.

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8. If h = 10 cm, c = 6 cm, b = 12 cm, d = 4 cm, find the values of each of its parts separately and add to find the area WXYZ. Verify it by putting the values of h, a and b in the expression