# Samacheer Kalvi 7th Maths Solutions Term 1 Chapter 2 Measurements Ex 2.1

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## Tamilnadu Samacheer Kalvi 7th Maths Solutions Term 1 Chapter 2 Measurements Ex 2.1

Question 1.
Find the area and perimeter of the following parallelograms. Solution:
(i) Given base b = 11 cm ; height h = 3 cm
Area of the parallelogram = b × h sq. units = 11 × 3 cm2
= 33 cm2
Also perimeter of a parallelogram = Sum of 4 sides
= 11 cm + 4 cm + 11 cm + 4 cm = 30 cm
Area = 33 cm2; Perimeter = 30 cm.

(ii) Given base b = 7 cm
height h = 10 cm
Area of the parallelogram = b × h sq. units
= 7 × 10 cm2 = 70 cm2
Perimeter = Sum of four sides
= 13 cm + 7 cm + 13 cm + 7 cm = 40 cm
Area = 70 cm2, Perimeter = 40 cm

Question 2.
Find the missing values. Solution:
(i) Given Base 6 = 18 cm ; Height h = 5 cm
Area of the parallelogram = b × h sq. units
= 18 × 5 cm2
= 90 cm2

(ii) Base b = 8m; Area of the parallelogram = 56 sq. m
b × h = 56
8 × A = 56
h = $$\frac{56}{8}$$
h = 7 m

(iii) Given Height h = 17 mm
Area of the parallelogram = 221 sq. mm
b × h = 221
b × 17 = 221
b = $$\frac{221}{17}$$
b = 13 m
Tabulating the results, we get Question 3.
Suresh on 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:
Given base 6 = 21 cm
Area of parallelogram = 735 sq. cm
b × h = 735
21 × h = 735
h = $$\frac{735}{21}$$
h = 35 cm
∴ Height of the trophy = 35 cm Question 4.
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: Area of a parallelogram = (base × height) sq. units
Base length = $$\frac{18}{2}$$ = 9 m
Height = $$\frac{12}{2}$$ = 6 m
Area = 9 × 6 = 54 m2
Area of each parallelogram = 54 m2

Question 5.
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 of the parallelogram h = 14 m
Base = 8 m longer than height
= (14 + 8) m = 22 m
Area of the parallelogram = (base × height) sq. units
= (22 × 14)m2 = 308 m2
Cost of levelling 1 m2 = ₹ 15
Cost of levelling 308 m2 = 308 × 15 = ₹ 4,620
Cost of levelling the ground = ₹ 4,620

Objective Type Questions

Question 6.
The perimeter of a parallelogram whose adjacent sides are 6 cm and 5 cm is
(i) 12 cm
(ii) 10 cm
(iii) 24 cm
(iv) 22 cm
Solution:
(iv) 22 cm
Hint:
= 2(6 + 5) = 2 × 11 = 22 cm

Question 7.
The area of parallelogram whose base 10 m and height 7 m is
(i) 70 sq.m
(ii) 35 sq.m
(iii) 7 sq.m
(iv) 10 sq.m
Solution:
(i) 70 sq. m
Hint: = base × height = 10m × 7m = 70 sq.m

Question 8.
The base of the parallelogram with area is 52 sq. cm and height 4 cm is
(i) 48 cm
(ii) 104 cm
(iii) 13 cm
(iv) 26 cm
Solution:
(iii) 13 cm
Hint: Question 9.
What happens to the area of the parallelogram if the base is increased 2 times and the height is halved?
(i) Decreases to half
(ii) Remains the same
(iii) Increase by two times
(iv) None
Solution:
(ii) Remains the same
Hint:
Area = b × h sq. units
New base = 2 × old base
New height = $$\frac{1}{2}$$ × old height
New Area = New base × New height = (2 × b)$$\frac{1}{2}$$ × h = bh = old Area. Question 10.
In a parallelogram the base is three times its height. If the height is 8 cm then the area is
(i) 64 sq. cm
(ii) 192 sq. cm
(iii) 32 sq. cm
(iv) 72 sq. cm
Solution:
(ii) 192 sq. cm
Hint: Given b = 3 × h; h = 8 cm
Area = b × h = 3h × 8 = 3 × 8 × 8 = 192 cm2