2 Mark Question

Question 12 Marks

Find the area of the triangle in which
Base = 42cm and height = 25cm.

Answer

Base of the triangle = 42cm

Height = 25cm
Area $=\frac{1}{2}\times\text{base}\times\text{height}$
$=\frac{1}{2}\times42\times25=525\text{cm}^2$

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Question 22 Marks

Find the circumference of a circle whose radius is:
28cm.

Answer

Radius of the circle (r) = 28cm
$\therefore\text{Circumference}=2\pi\text{r}$
$=2\times\frac{22}{7}\times28\text{cm}$
$=176\text{cm}$

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Question 32 Marks

Find the area of the square, the length of whose diagonal is:
72cm.

Answer

Diagonal of the square = 72cm
$\therefore$ Area of the square $=\Big[\frac{1}{2}\times(\text{Diagonal})^2\Big]\text{sq. unit}$
$=\Big[\frac{1}2{}\times(72)^2\Big]\text{cm}^2$
$=2592\text{cm}^2$

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Question 42 Marks

Find the area of the triangle in which
Base = 16.8m and Height = 75cm.

Answer

Base of the triangle = 16.8m
and height = 75cm = 0.75m
Area $=\frac{1}{2}\times\text{Base}\times\text{Height}$
$=\frac{1}{2}\times16.8\times0.75\text{m}^2=6.3\text{m}^2$

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Question 52 Marks

Find the height of a parallelogram whose area is $54 cm^2$ and the base is 15 cm .

Answer

Area of the given parallelogram $=54 cm^2$
Base of the given parallelogram $=15 cm$
$\therefore$ Height of the given parallelogram $=\frac{\text { Area }}{\text { Base }}$
$=\left(\frac{54}{15}\right) cm=3.6 cm$

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Question 62 Marks

Find the area of a rhombus in which
Each side $=2 dm$ and height $=12.6 cm$.

Answer

A rhombus is a special type of a parallelogram.
Base $=2 dm =(2 \times 10)=20 cm$ [since $1 dm =10 cm$ ]
Height $=12.6 cm$
$\therefore$ Area of the rhombus $=20 cm \times 12.6 cm=252 cm^2$

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Question 72 Marks

Find the radius of a circle whose circumference is 57.2cm.

Answer

Circumference of a circle (c) = 57.2cm
$\therefore\text{Radius}=\frac{\text{c}}{2\pi}=\frac{57.2\times7}{2\times22}\text{cm}=\frac{2.6\times7}{2}$
$=9.1\text{cm}$

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Question 82 Marks

In a parallelogram it is being given that base $=14 dm$ and height $=6.5 dm$. Find its area in:
$cm^2$

Answer

Base $=14 dm =(14 \times 10) cm =140 cm$ [since $1 dm =10 cm$ ]
Height $=6.5 dm =(6.5 \times 10) cm =65 cm$
Area of the parallelogram $=$ Base $\times$ Height
$=140 cm \times 65 cm$
$=9100 cm^2$

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Question 92 Marks

Find the area of a square, the length of whose diagonal is 64cm.

Answer

Given that the diagonal of a square is 64 cm
Area of the square $=\frac{(\text { Diagonal })^2}{2}$
$=\frac{(64)^2}{2}=\frac{4096}{2}=2048 cm^2$
Area of the square $=2048 cm^2$

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Question 102 Marks

Find the area of the triangle in which
Base = 8dm and Height = 35cm.

Answer

Base of a triangle (b) = 8m = 80cm
and height (h) = 35cm
Area $=\frac{1}{2}\text{bh}=\frac{1}{2}\times80\times35=1400\text{cm}^2$

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Question 112 Marks

Find the height of a triangle region having an area of $224 m^2$ and base 28 m .

Answer

Area of triangular region $=224 m^2$
Base $=28 m$
$\therefore \text { Height }=\frac{\text { Area } \times 2}{\text { Base }}$
$=\frac{224 \times 2}{28}$
$=16 m$

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Question 122 Marks

Find the area of an equilateral triangle each of whose sides measures:
18cm [Take $\sqrt{3}=1.73$]

Answer

Side of the equilateral triangle (a) = 18cm
$\therefore\text{Area}=\frac{\sqrt{3}}{4}\text{a}^2=\frac{\sqrt{3}}{4}\times(18)^2\text{cm}^2$

$=\frac{\sqrt{3}}4{}\times18\times18=81(1.73)\text{cm}^2$
$=140.13\text{cm}^2$

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Question 132 Marks

Find the base of a triangle whose are is $90 cm^2$ and height 12 cm .

Answer

Area of triangle $=90 cm^2$
and height $( h )=12 cm$
$\therefore$ Base $=\frac{\text { Area } \times 2}{\text { Height }}$
$=\frac{90 \times 2}{12}=15 cm$

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Question 142 Marks

Find the area of an equilateral triangle each of whose sides measures:
20cm [Take $\sqrt{3}=1.73$]

Answer

Each side of equilateral triangle (a)
= 20cm
$\therefore\text{Area}=\frac{\sqrt{3}}{4}\text{a}^2=\frac{\sqrt{3}}{4}\times20\times20\text{cm}^2$
$=1.73\times100=173\text{cm}^2$

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Question 152 Marks

Find the area of a circle whose diameter is:
28cm.

Answer

Diameter of the circle $=28\text{cm}$
$\therefore\text{Radius}(\text{r})=\frac{28}{2}=14\text{cm}$
and Area $=\pi\text{r}^2=\frac{22}{7}\times14\times14\text{cm}^2$
$=616\text{cm}^2$

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Question 162 Marks

Find the area of the square, the length of whose diagonal is:
2.4m.

Answer

Diagonal of the square = 2.4m
$\therefore$ Area of the square $=\Big[\frac{1}{2}\times(\text{Diagonal})^2\Big]\text{sq. unit}$
$=\Big[\frac{1}{2}\times(2.4)^2\Big]\text{m}^2$
$=2.88\text{m}^2$

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Question 172 Marks

The base of a parallelogram measures 1 m 60 cm and its height is 75 cm . Find its area in $m ^2$.

Answer

Base $=1 m 60 cm=1.6 m$ [since $100 cm=1 m]$
Height $=75 cm=0.75 m$
$\therefore$ Area of the parallelogram $=$ Base $\times$ Height
$=1.6 m \times 0.75 m$
$=1.2 m^2$

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Question 182 Marks

Find the circumference of a circle whose diameter is:
4.9m.

Answer

Diameter of circle (d) = 4.9m
$\therefore\text{Circumference}=\text{d}\pi=\frac{4.9\times22}{7}\text{cm}$
$=7\times22=154\text{m}$

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Question 192 Marks

Find the area of a circle whose radius is:
3.5m.

Answer

Radius of the circle (r) $=3.5\text{m}$
$\therefore\text{Area}=\pi\text{r}^2=\frac{22}{7}\times3.5\times3.5\text{m}^2$
$=38.5\text{m}^2$

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Question 202 Marks

The area of an equilateral triangle is $(16\times\sqrt{3})\text{cm}^2.$ Find the length of each side the triangle.

Answer

Area of equilateral triangle $=16\sqrt{3}\text{cm}^2$
Let each side = a
Then $\frac{\sqrt{3}}{4}\text{a}^2=16\sqrt{3}$
$\Rightarrow\text{a}^2=\frac{16\sqrt{3}\times4}{\sqrt{3}}$
$\Rightarrow\text{a}^2=64=(8)^2$
$\text{a}=8\text{cm}$
Each side $=8\text{cm}$

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Question 212 Marks

Find the area of a rhombus in which
Each side $=12 cm$ and height $=7.5 cm$.

Answer

A rhombus is a special type of a parallelogram.
The area of a parallelogram is given by the product of its base and height.
$\therefore$ Area of the given rhombus $=$ Base $\times$ Height
Area of the rhombus $=12 cm \times 7.5 cm=90 cm^2$

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Question 222 Marks

Find the area of a parallelogram with base 32cm and height 16.5cm.

Answer

Base $=32 cm$
Height $=16.5 cm$
$\therefore$ Area of the parallelogram = Base × Height
$=32 cm \times 16.5 cm$
$=528 cm^2$

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Question 232 Marks

Find the length of the height of an equilateral triangle of side 24cm. [Take $\sqrt{3}=1.73$]
Hint $\frac{1}{2}\times24\times\text{h}=\frac{\sqrt{3}}{4}\times24\times24.$ Find h.

Answer

Each side of an equilateral triangle = 24cm
Length of altitude $=\frac{\sqrt{3}}{2}\text{a}=\frac{\sqrt{3}}{2}\times24$
$=12\sqrt{3}\text{cm}=12(1.73)=20.76\text{cm}$

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Question 242 Marks

Find the circumference of a circle whose diameter is:
35cm.

Answer

Diameter of circle (d) = 35cm
$\therefore\text{Circumference}=\text{d}\pi=\frac{35\times22}{7}\text{cm}$
$=110\text{cm}$

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Question 252 Marks

Find the height of a triangle having an area of $72 cm^2$ and base 16 cm .

Answer

Base of triangle $=16 cm$
area of the triangle $=72 cm^2$
$\therefore \text { Height }=\frac{\text { Area } \times 2}{\text { Base }}$
$=\frac{72 \times 2}{16}$
$=9 cm$

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Question 262 Marks

Find the area of a circle whose diameter is:
1.4m.

Answer

Diameter of the circle $=1.4\text{cm}$
$\therefore\text{Radius}(\text{r})=\frac{1.4}{2}=0.7\text{cm}$
$\therefore\text{Area}=\pi\text{r}^2=\frac{22}{7}\times0.7\times0.7\text{cm}^2$
$=1.54\text{m}^2$

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Question 272 Marks

Find the circumference of a circle of radius 15 cm. (Take $\pi$ = 3.14.)

Answer

Radius of a circle = 15cm

Circumference $=2\pi\text{r}=2\times3.14\times15=94.20\text{cm}$
$=94.2\text{cm}$

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Question 282 Marks

Find the diameter of a circle whose circumference is 63.8m.

Answer

Circumference (c) = 63.8m
$\therefore\text{Diameter}=\frac{\text{c}}{\pi}=\frac{63.8\times7}{22}\text{m}=2.9\times7$
$=20.3\text{m}$

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Question 292 Marks

Find the circumference of a circle whose radius is:
1.4m.

Answer

Radius of the circle (r) = 1.4m
$\therefore\text{Circumference}=2\pi\text{r}$
$=2\times\frac{22}{7}\times1.4\text{m}$
$=2\times\frac{22}{7}\times\frac{14}{10}\text{m}=\frac{44}{5}=8.8\text{m}$

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Question 302 Marks

Find the area of a square each of whose sides measures 8.5m.

Answer

Side of square (a) $=8.5 m$
Area$=a^2=(8.5)^2=8.5 \times 8.5 m^2=72.25 m^2$

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Question 312 Marks

Find the area of the rectangle whose dlmensions are:
length $=12.5 m$, breadth $=8 dm$.

Answer

Length of rectangle $( I )=12.5 m$
Breadth (b) $=8 cm=0.80 m$
Area $=I \times b=12.5 \times 0.80 m^2=10 m^2$

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Question 322 Marks

In a parallelogram it is being given that base $=14 dm$ and height $=6.5 dm$. Find its area in:
$m^2$.

Answer

Base $=14 dm =(14 \times 10) cm$ [since $1 dm =10 cm$ and $100 cm=1 m$ ]
$=140 cm=1.4 m$
Height $=6.5 dm =(6.5 \times 10) cm$
$=65 cm=0.65 m$
$\therefore$ Area of the parallelogram $=$ Base $\times$ Height
$=1.4 m \times 0.65 m$
$=0.91 m^2$

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Question 332 Marks

Find the area of a circle whose radius is:
21cm.

Answer

Radius of the circle (r) $=21\text{cm}$
$\therefore\text{Area}=\pi\text{r}^2=\frac{22}{7}\times21\times21\text{cm}^2$
$=1386\text{cm}^2$

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Question 342 Marks

Find the area of the rectangle whose dlmensions are: length = 24.5m, breadth = 18m

Answer

Length of rectangle (l) = 24.5m Breadth (b) = 18m

Area $=\mid \times b=24.5 \times 18 m^2=441 m^2$

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