The DAV Maths Class 7 Solutions and **DAV Class 7 Maths Chapter 11 Worksheet 3** Solutions of Perimeter and Area offer comprehensive answers to textbook questions.

## DAV Class 7 Maths Ch 11 WS 3 Solutions

Question 1.

One side of a parallelogram is 14 cm. Its distance from the opposite sides is 16.5 cm. Find the area of parallelogram.

Answer:

Area of the parallelogram

= Base x Distance between the parallel sides

= 14 cm x 16.5 cm

= 231 cm^{2}

Question 2.

A parallelogram has a base of 135 dm. The corresponding height is 6 cm. Find the area of the parallelogram in square metres.

Answer:

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Area of the parallelogram = Base × Height

= 135 dm x 6 dm

= 810 dm^{2}

= 8.10 m^{2}

Hence the required area = 8.1 m^{2} .

Question 3.

The altitude of a parallelogram corresponding to a base of length 15 cm is 18 cm. Find the area of the parallelogram.

Answer:

Area of the parallelogram = Base × Altitude

= 15 × 18 = 270 cm^{2}

Hence the required area = 270 cm^{2}.

Question 4.

The height of parallelogram is 3 dm. If the area is 240 cm2, find the base of the parallelogram.

Answer:

Height h = 3 dm = 30 cm and area = 240 cm^{2}

Area of parallelogram = Base × Height

240 = Base × 30

Base = \(\frac{240}{30}\) = 8 cm

Hence the required base = 8 cm.

Question 5.

Find the area of rhombus whose one side is 8 cm and altitude is 0.6 dm.

Answer:

One side of rhombus = 8 cm

Altitude = 0.6 dm = 0.6 × 10 = 6 cm

Area = Side × Altitude = 8 × 6 = 48 cm^{2}

Hence the required area = 48 cm^{2}.

Question 6.

Find the altitude of a rhombus whose area is 320 m^{2} and side is 5 m.

Answer:

Area of rhombus = 320 m^{2} and side = 5 m

Area = side × altitude 320 = 5 × altitude

∴ Altitude = \(\frac{240}{30}\) = 64 cm

Hence the required altitude = 64 cm.

Question 7.

The height of parallelogram is one-third of its base. If the area is 108 cm2, find the base and height.

Answer:

Let the base be x cm

its height = \(\frac{1}{3}\) x cm

Area = base × height

⇒ 108 = x × \(\frac{1}{3}\)x

⇒ 108 = \(\frac{x^2}{3}\)

⇒ x^{2} = 108 × 3

⇒ x^{2} = 324

x = 18 cm

Hence base = 18 cm and the height = 18 × y = 6 cm.

Question 8.

The area of a rhombus is 119 cm^{2} and its perimeter is 56 cm. Find its altitude.

Answer:

Perimeter of rhombus = 56 cm.

Its one side = \(\frac{56}{4}\) = 14 cm

Area = side × altitude 119

= 14 × altitude

Altitude = \(\frac{119}{14}\) = 8.5 cm

Hence the required altitude = 8.5 cm.

Question 9.

One side and corresponding altitude of a parallelogram are 50 an and 8 cm. If the other altitude is 4 cm, find the length of the other pair of parallel sides.

Answer:

Area of the parallelogram = Side × corresponding altitude

= 50 × 8 = 400 cm^{2}

Now other altitude corresponding to other side = 4 cm

Area = Side × Altitude

400 = Side × 4

∴ Side = = 100 cm

Hence the required side = 100 cm.

Question 10.

Area of a parallelogram is 625 m^{2}. Find the length of sides of parallelogram if altitude corresponding to sides are 20 m and 25 m.

Answer:

Let the length of the side corresponding to altitude 20 m be x m and corresponding to 25 m be y m.

Area = base × altitude

625 = x × 20

x = \(\frac{625}{20}\) = 31.25 m

Area = base × altitude

625 = y × 25

∴ y = \(\frac{625}{20}\) = 25 m

Hence the required length of sides are 31.25 m and 25 m.