Exercise 2.1 - Chapter 2 Measurements Term 1 7th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated On August 15, 2024

By SaraNextGen

Ex $2.1$
Question $1 .$
Find the area and perimeter of the following parallelograms.

Solution:
(i) Given base $b=11 \mathrm{~cm}$; height $h=3 \mathrm{~cm}$
Area of the parallelogram $=\mathrm{b} \times \mathrm{h}$ sq. units $=11 \times 3 \mathrm{~cm}^{2}$ $=33 \mathrm{~cm}^{2}$
Also perimeter of a parallelogram $=$ Sum of 4 sides $=11 \mathrm{~cm}+4 \mathrm{~cm}+11 \mathrm{~cm}+4 \mathrm{~cm}=30 \mathrm{~cm}$
Area $=33 \mathrm{~cm}^{2} ;$ Perimeter $=30 \mathrm{~cm} .$
(ii) Given base $b=7 \mathrm{~cm}$
height $\mathrm{h}=10 \mathrm{~cm}$
Area of the parallelogram $=\mathrm{b} \times \mathrm{h}$ sq. units
$=7 \times 10 \mathrm{~cm}^{2}=70 \mathrm{~cm}^{2}$
Perimeter $=$ Sum of four sides
$=13 \mathrm{~cm}+7 \mathrm{~cm}+13 \mathrm{~cm}+7 \mathrm{~cm}=40 \mathrm{~cm}$
Area $=70 \mathrm{~cm}^{2}$, Perimeter $=40 \mathrm{~cm}$

Question 2

Find the missing values.

Solution:
(i) Given Base $6=18 \mathrm{~cm}$; Height $\mathrm{h}=5 \mathrm{~cm}$
Area of the parallelogram $=\mathrm{b} \times \mathrm{h}$ sq. units
$\begin{aligned}
&=18 \times 5 \mathrm{~cm}^{2} \\
&=90 \mathrm{~cm}^{2}
\end{aligned}$
(ii) Base $\mathrm{b}=8 \mathrm{~m}$; Area of the parallelogram $=56 \mathrm{sq}$. $\mathrm{m}$
$\begin{aligned}
&\mathrm{b} \times \mathrm{h}=56 \\
&8 \times \mathrm{A}=56 \\
&\mathrm{~h}=\frac{56}{8} \\
&\mathrm{~h}=7 \mathrm{~m}
\end{aligned}$
(iii) Given Height $\mathrm{h}=17 \mathrm{~mm}$
Area of the parallelogram $=221$ sq. $\mathrm{mm}$
$\begin{aligned}
&\mathrm{b} \times \mathrm{h}=221 \\
&\mathrm{~b} \times 17=221 \\
&\mathrm{~b}=\frac{221}{17} \\
&\mathrm{~b}=13 \mathrm{~m}
\end{aligned}$

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 $6=21 \mathrm{~cm}$
Area of parallelogram $=735$ sq. $\mathrm{cm}$
$\mathrm{b} \times \mathrm{h}=735$
$21 \times \mathrm{h}=735$
$\begin{aligned}
&\mathrm{h}=\frac{735}{21} \\
&\mathrm{~h}=35 \mathrm{~cm}
\end{aligned}$
$\therefore$ Height of the trophy $=35 \mathrm{~cm}$

Question $4 .$
Janaki has a piece of fabric in the shape of a parallelogram. Its height is $12 \mathrm{~m}$ and its base is $18 \mathrm{~m}$. She cuts the fabric into four equal parallelograms by cutting the parallel sides through its midpoints. Find the area of each new parallelogram.
Solution:

Area of a parallelogram $=($ base $\times$ height $)$ sq. units
Base length $=\frac{18}{2}=9 \mathrm{~m}$
Height $=\frac{12}{2}=6 \mathrm{~m}$
Area $=9 \times 6=54 \mathrm{~m}^{2}$
Area of each parallelogram $=54 \mathrm{~m}^{2}$

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. $\mathrm{m}$.
Solution:

Height of the parallelogram $\mathrm{h}=14 \mathrm{~m}$
Base $=8 \mathrm{~m}$ longer than height
$=(14+8) \mathrm{m}=22 \mathrm{~m}$
Area of the parallelogram $=$ (base $\times$ height) sq. units $=(22 \times 14) \mathrm{m}^{2}=308 \mathrm{~m}^{2}$
Cost of levelling $1 \mathrm{~m}^{2}=₹ 15$
Cost of levelling $308 \mathrm{~m}^{2}=308 \times 15=₹ 4,620$
Cost of levelling the ground $=₹ 4,620$

Objective Type Questions
Question 6 .
The perimeter of a parallelogram whose adjacent sides are $6 \mathrm{~cm}$ and $5 \mathrm{~cm}$ is
(i) $12 \mathrm{~cm}$
(ii) $10 \mathrm{~cm}$
(iii) $24 \mathrm{~cm}$
(iv) $22 \mathrm{~cm}$
Solution:
(iv) $22 \mathrm{~cm}$
Hint:
$=2(6+5)=2 \times 11=22 \mathrm{~cm}$
 

Question $7 .$
The area of parallelogram whose base $10 \mathrm{~m}$ and height $7 \mathrm{~m}$ is
(i) 70 sq.m
(ii) 35 sq.m
(iii) $7 \mathrm{sq} \cdot \mathrm{m}$
(iv) 10 sq.m

Solution:
(i) 70 sq. $\mathrm{m}$
Hint: $=$ base $\times$ height $=10 \mathrm{~m} \times 7 \mathrm{~m}=70$ sq.m

Question $8 .$
The base of the parallelogram with area is $52 \mathrm{sq} . \mathrm{cm}$ and height $4 \mathrm{~cm}$ is
(i) $48 \mathrm{~cm}$
(ii) $104 \mathrm{~cm}$
(iii) $13 \mathrm{~cm}$
(iv) $26 \mathrm{~cm}$
Solution:
(iii) $13 \mathrm{~cm}$
Hint:
base $=\frac{\text { area }}{\text { height }}=\frac{52 \mathrm{sq} \cdot \mathrm{cm}}{4 \mathrm{~cm}}=13 \mathrm{~cm}$

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

Question $10 .$
In a parallelogram the base is three times its height. If the height is $8 \mathrm{~cm}$ then the area is
(i) 64 sq. $\mathrm{cm}$
(ii) 192 sq. $\mathrm{cm}$
(iii) $32 \mathrm{sq} . \mathrm{cm}$
(iv) $72 \mathrm{sq.} \mathrm{cm}$
Solution:
(ii) 192 sq. $\mathrm{cm}$