SChand Composite Mathematics Class 7 Chapter 14 Perimeter and Area Exercise 14C

  Exercise 14 C

Question 1 

Find the area of each parallelogram.

$\begin{array}{|l|l|l|l|l|l|}\hline & \text { (i) } & \text { (ii) } & \text { (iii) } & \text { (iv) } & \text { (v) } \\\hline \text { Base } & 8 \mathrm{~cm} & 12 \mathrm{~mm} & 6.5 \mathrm{~m} & 1 \mathrm{~m}5 \cdot \mathrm{cm} & 4.2 \mathrm{dm} \\\hline \text { Height } & 3 \mathrm{~cm} & 8.7 \mathrm{~cm} & 4.8 \mathrm{~m} & 45\mathrm{~cm} & 25 \mathrm{~cm} \\\hline\end{array}$

 (i) Area = $=B \times H$

$=8 \times 3$

$=24 \mathrm{~cm}^{2}$

(ii) Base $212 \mathrm{~mm}$

$1 c m=10 \mathrm{~mm}$

B= 1.2cm 

Area = $=B \times H$

$=1.2 \times 3.7=10.44\mathrm{~cm}2$

(iii) 

$\begin{aligned} A &=B \times H \\ &=6.5 \times 4.8 \\ &=31.20 \\ & m^{2} \end{aligned}$

(iv) $1 m=100 \mathrm{~cm}$

$B=105 \mathrm{~cm}$

Area $=105 \times 45^{-}$

$=4725 \mathrm{~cm}^{2}$ $=0.4725 \mathrm{~m}^{2}$

Question 2

(i) Area of ||gm ABCD = $48 \mathrm{~cm}^{2}$ DE = 6cm AB =? 

(DIAGRAM TO BE ADDED)

Sol: Area $=B \times 4$

$\begin{aligned}&48=D E \times A B \\&A B=\frac{43}{6} \\&A B=8 \mathrm{~cm}\end{aligned}$

(ii) 

Area of $\| \mathrm{gm}$ PQRS $=252 \mathrm{~cm}^{2}$ PQ = 9CM RT= ? 

Sol: 

$\begin{aligned} \text { Area } &=P Q \times RT \\ \Rightarrow 252 &=9 \times R T \\ \Rightarrow R T &=\frac{252}{9} \Rightarrow R T=28 \mathrm{~cm} \end{aligned}$

Question 3

The side of a rhombs is 7.2cm and its altitude is 5cm. Find its area. 

[Hint. Since a rhombus is a parallelogram with all its sides equal, the formula for area of a ||gm is applicable to it also]

Sol: Area = Base $ \times $ Height (altitude)

$=7.2 \times 5$

$=36 \mathrm{~cm}^{2}$

Question 4

The adjacent sides of a parallelogram are 36 cm and 27cm in length . if the perpendicular distance between the shorter sides is 12 cm, find the distacne between the longer sides. 

(IMAGE TO BE ADDED)

Sol: Given AE = 12CM 

Area of parallelogram ABCD = BASE $\times$ height 

$=D C \times A E$

$=27 \times 12 \mathrm{~cm}^{2}$

As we know Area of ||gm ABCD = $ BC \times AF $ = $DC \times AE $

$\Rightarrow A F=\frac{27 \times 12}{36} \Rightarrow A F=9 \mathrm{~cm}$,

Question 5

The area of a parallelogram and a square are the same. If the perimeter of the square is $160 \mathrm{~m}$ and the height of the parallelogram is $20 \mathrm{~m}$, find the length of the corresponding base of the parallelogram.

Sol: Perimeter of square = 160 m 

$4 \times$ side $=160 \Rightarrow$ side $=\frac{160}{4}$ =  Side = 40 m

Area of square = side $^{2}$ $=40^{2}=1600 \mathrm{~m}^{2}$

Area of parallelogram = Base $ \times $ Height $=1600$

$\Rightarrow$ Base $=\frac{1600}{20}$

 Base $=80 \mathrm{~m}$

Question 6

The area of a rhombus is $42 \mathrm{~m}^{2}$. If its perimeter is $24 \mathrm{~m}$, find its altitude.

Sol: Perimeter = 24 m 

$4 \times $ side $=24 \Rightarrow$ side $=6 \mathrm{~m}$

Area = Base $ \times $ Height= 42

Height = $\frac{42}{6}$

H= 7m answer