7 th maths chapter 2 || 2.1

 

7th Standard Mathematics — Chapter 2: Measurements

Exercise 2.1 Solutions

1. Find the area and perimeter of the following parallelograms

1. Figure (i):
   Given: Base (b) = 11 cm, Height (h) = 3 cm, Adjacent side = 4 cm
   
   Area of Parallelogram = base × height
   
   • Area = 11 cm × 3 cm = 33 sq. cm
   
   Perimeter = 2 × (Sum of adjacent sides)
   
   • Perimeter = 2 × (11 cm + 4 cm) = 2 × 15 cm = 30 cm
   Answer: Area = 33 sq. cm, Perimeter = 30 cm


2. Figure (ii):
   Given: Base (b) = 7 cm, Height (h) = 10 cm, Adjacent side = 13 cm
   • Area = base × height = 7 cm × 10 cm = 70 sq. cm
   • Perimeter = 2 × (7 cm + 13 cm) = 2 × 20 cm = 40 cm
   Answer: Area = 70 sq. cm, Perimeter = 40 cm

2. Find the missing values

S.No.	Base (b)	Height (h)	Area (b × h)
(i)	18 cm	5 cm	90 sq. cm
(ii)	8 m	7 m	56 sq. m
(iii)	13 mm	17 mm	221 sq. mm

Workings:

• (i) Area: 18 cm × 5 cm = 90 sq. cm
• (ii) Height: Area ÷ Base = 56 sq. m ÷ 8 m = 7 m
• (iii) Base: Area ÷ Height = 221 sq. mm ÷ 17 mm = 13 mm

3. Trophy Height Problem

Suresh won a parallelogram-shaped trophy in a state level Chess tournament. He knows that the area of the trophy is 735 sq. cm and its base is 21 cm. What is the height of that trophy?

Solution:

• Area of trophy = 735 sq. cm
• Base (b) = 21 cm
• Height (h) = Area ÷ Base

Calculation: h = 735 ÷ 21 = 35 cm

Answer: The height of the trophy is 35 cm.

4. Fabric Cutting Problem

Janaki has a piece of fabric in the shape of a parallelogram. Its height is 12 m and its base is 18 m. She cuts the fabric into four equal parallelograms by cutting the parallel sides through its mid-points. Find the area of each new parallelogram.

Solution:

• Height of original fabric = 12 m
• Base of original fabric = 18 m
• Total Area of fabric = base × height = 18 m × 12 m = 216 sq. m

Since the fabric is cut into 4 equal parallelograms:

Area of each new parallelogram = Total Area ÷ 4 = 216 ÷ 4 = 54 sq. m

Answer: The area of each new parallelogram is 54 sq. m.

5. Ground Levelling Cost Problem

A ground is in the shape of parallelogram. The height of the parallelogram is 14 metres and the corresponding base is 8 metres longer than its height. Find the cost of levelling the ground at the rate of ₹ 15 per sq. m.

Solution:

• Height (h) = 14 m
• Base (b) = Height + 8 m = 14 + 8 = 22 m
• Area of the ground = base × height = 22 m × 14 m = 308 sq. m
• Rate of levelling = ₹ 15 per sq. m

Calculation: Total Cost = 308 sq. m × ₹ 15 = ₹ 4,620

Answer: The cost of levelling the ground is ₹ 4,620.