The DAV Maths Class 7 Solutions and **DAV Class 7 Maths Chapter 11 Worksheet 2** Solutions of Perimeter and Area offer comprehensive answers to textbook questions.

## DAV Class 7 Maths Ch 11 WS 2 Solutions

Question 1.

The given figure, shows two paths drawn inside a rectangular field 50 m long and 35 m wide. The width of the path is 5 m. Find the area of the shaded portion.

Answer:

Area of the path along the length of the rectangle = 50 × 5 = 250 m^{2}

Area of the path along the width of the rectangle

= 35 × 5 = 175 m^{2}

Area of the common portion = 5 × 5 = 25 m^{2}

∴ Total area of the two paths (shaded)

= (250 m^{2} + 175 m^{2}) – 25 m^{2}

= 425 m^{2} – 25 m^{2}

= 400 m^{2}

Hence the required area = 400 m^{2}.

Question 2.

An oblong garden measures 60 m by 55 m. From the centre of each side, a path 2 meters wide goes across to the centre of the opposite side. Find the area of the paths.

Answer:

Area of the path along length = 60 × 2 = 120 m^{2}

Area of the path along breadth = 55 × 2 = 110 m^{2}

Area of the common portion = 2 × 2 = 4 m^{2}

Area of the paths = 120 m^{2} + 110 m^{2} – 4 m^{2}

= 230 m^{2} – 4 m^{2}

= 226 m^{2}

Hence the area of the two path = 226 m^{2}.

Question 3.

A rectangular plot of land is 300 m long and 250 m broad. It has two roads, each 3 m wide running midway within it, one parallel to the length and the other parallel to the breadth. Find the area of the roads. Also calculate the cost of constructing the roads at ₹ 50 per square meter.

Answer:

Area of the road along the length of the plot

= 300 m × 3 m

= 900 m^{2}

Area of the road along the width of the plot = 250 m × 3 m

= 750 m^{2}

Area of the common portion = 3m × 3m

= 9m^{2}

Area of the roads = 900 m^{2} + 750 m^{2} – 9 m^{2}

= 1650 m^{2} – 9 m^{2}

= 1641 m^{2}

Cost of construction = 1641 × 50

= ₹ 82050

Hence the required area = 1641 m^{2} and the required cost = ₹ 82050.

Question 4.

A rectangular piece of ground is 45 m long and 30 m wide. It has two roads each 1 m wide, running midway within it, one parallel to the length and the other parallel to the breadth. Find the area of roads. Also calculate the area of the remaining ground.

Answer:

Area of the rectangular ground = 45 m × 30 m = 1350 m^{2}

Area of the road along the length

= 45 m × 1 m = 45 m^{2}

Area of the road along the breadth = 30 m × 1 m

= 30 m^{2}

Area of the common portion = 1 × 1

= 1 m^{2}

Area of the roads = 45 m^{2} + 30 m^{2} – 1 m^{2}

= 74 m^{2}

Area of the remaining ground = 1350 m^{2} – 74 m^{2}

= 1276 m^{2}

Hence the required area of the roads = 74 m^{2} and the required area of the ground = 1276 m^{2}.