DAV Class 7 Maths Chapter 11 Worksheet 3 Solutions

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 cm²

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:
im-1
Area of the parallelogram = Base × Height
= 135 dm x 6 dm
= 810 dm²
= 8.10 m²
Hence the required area = 8.1 m² .

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 cm²
Hence the required area = 270 cm².

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 cm²
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 cm²
Hence the required area = 48 cm².

Question 6.
Find the altitude of a rhombus whose area is 320 m² and side is 5 m.
Answer:
Area of rhombus = 320 m² 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 = \(\frac{x^2}{3}\)
⇒ x² = 108 × 3
⇒ x² = 324
x = 18 cm
Hence base = 18 cm and the height = 18 × y = 6 cm.

Question 8.
The area of a rhombus is 119 cm² 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 cm²
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 m². 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.