Question 12 Marks
Find the area of the triangle in which Base $= 42\ cm$ and height $= 25\ cm.$
AnswerBase of the triangle $= 42\ cm$
Height = 25cm Area $=\frac{1}{2}\times\text{base}\times\text{height}$
$=\frac{1}{2}\times42\times25=525\text{cm}^2$ View full question & answer→Question 22 Marks
Find the circumference of a circle whose radius is: $28\ cm.$
AnswerRadius of the circle $(r) = 28\ cm$
$\therefore\text{Circumference}=2\pi\text{r}$
$=2\times\frac{22}{7}\times28\text{cm}$
$=176\text{cm}$
View full question & answer→Question 32 Marks
Find the area of the square, the length of whose diagonal is: $72\ cm.$
AnswerDiagonal of the square $= 72\ cm$
$\therefore$ Area of the square $=\Big[\frac{1}{2}\times(\text{Diagonal})^2\Big]\text{sq. unit}$
$=\Big[\frac{1}2{}\times(72)^2\Big]\text{cm}^2$
$=2592\text{cm}^2$
View full question & answer→Question 42 Marks
Find the area of the triangle in which Base $= 16.8\ m$ and Height $= 75\ cm.$
AnswerBase of the triangle $= 16.8\ m$ and height $= 75\ cm = 0.75\ m$
Area $=\frac{1}{2}\times\text{Base}\times\text{Height}$
$=\frac{1}{2}\times16.8\times0.75\text{m}^2=6.3\text{m}^2$
View full question & answer→Question 52 Marks
Find the height of a parallelogram whose area is $54 \mathrm{~cm}^2$ and the base is $15\ cm.$
AnswerArea of the given parallelogram $= 54 \mathrm{~cm}^2$
Base of the given parallelogram $= 15\ cm$
$\therefore$ Height of the given parallelogram $=\frac{\text{Area}}{\text{Base}}$
$=\Big(\frac{54}{15}\Big)\text{cm}=3.6\text{cm}$
View full question & answer→Question 62 Marks
Find the area of a rhombus in which Each side $= 2dm$ and height $= 12.6\ cm.$
AnswerA rhombus is a special type of a parallelogram.
Base $=2 \mathrm{dm}=(2 \times 10)=20 \mathrm{~cm}[$ since $1 \mathrm{dm}=10 \mathrm{~cm}]$
Height $=12.6 \mathrm{~cm}$
$\therefore$ Area of the rhombus $=20 \mathrm{~cm} \times 12.6 \mathrm{~cm}=252 \mathrm{~cm}^2$
View full question & answer→Question 72 Marks
Find the radius of a circle whose circumference is $57.2\ cm.$
AnswerCircumference of a circle $(c) = 57.2cm$
$\therefore\text{Radius}=\frac{\text{c}}{2\pi}=\frac{57.2\times7}{2\times22}\text{cm}=\frac{2.6\times7}{2}$
$=9.1\text{cm}$
View full question & answer→Question 82 Marks
In a parallelogram it is being given that base $= 14dm$ and height $= 6.5dm$. Find its area in: $cm^2$.
Answer$\text { Base }=14 \mathrm{dm}=(14 \times 10) \mathrm{cm}=140 \mathrm{~cm}[\text { since } 1 \mathrm{dm}=10 \mathrm{~cm}]$
$ \text { Height }=6.5 \mathrm{dm}=(6.5 \times 10) \mathrm{cm}=65 \mathrm{~cm}$
$ \text { Area of the parallelogram }=\text { Base } \times \text { Height }$
$ =140 \mathrm{~cm} \times 65 \mathrm{~cm}$
$ =9100 \mathrm{~cm}^2$
View full question & answer→Question 92 Marks
Find the area of a square, the length of whose diagonal is $64\ cm.$
AnswerGiven that the diagonal of a square is $64\ cm$
Area of the square $=\frac{(\text{Diagonal})^2}{2}$
$=\frac{(64)^2}{2}=\frac{4096}{2}=2048\text{cm}^2$
Area of the square = $2048 \mathrm{~cm}^2$
View full question & answer→Question 102 Marks
Find the area of the triangle in which Base $= 8\ dm$ and Height $= 35\ cm.$
AnswerBase of a triangle $(b) = 8m = 80\ cm$ and height $(h) = 35\ cm$
Area $=\frac{1}{2}\text{bh}=\frac{1}{2}\times80\times35=1400\text{cm}^2$
View full question & answer→Question 112 Marks
Find the height of a triangle region having an area of $224 m^2$ and base $28\ m.$
AnswerArea of triangular region = $224 m^2$
Base $= 28\ m$
$\therefore\text{Height}
=\frac{\text{Area}\times2}{\text{Base}}$
$=\frac{224\times2}{28}$
$=16\text{m}$
View full question & answer→Question 122 Marks
Find the area of an equilateral triangle each of whose sides measures: 18cm [Take $\sqrt{3}=1.73$]
AnswerSide of the equilateral triangle (a) = 18cm $\therefore\text{Area}=\frac{\sqrt{3}}{4}\text{a}^2=\frac{\sqrt{3}}{4}\times(18)^2\text{cm}^2$ 
$=\frac{\sqrt{3}}4{}\times18\times18=81(1.73)\text{cm}^2$ $=140.13\text{cm}^2$ View full question & answer→Question 132 Marks
Find the base of a triangle whose are is $90 \mathrm{~cm}^2$ and height $12\ cm.$
AnswerArea of triangle = $90 \mathrm{~cm}^2$
and height $(h) = 12\ cm$
$\therefore\text{Base}=\frac{\text{Area}\times2}{\text{Height}}$
$=\frac{90\times2}{12}=15\text{cm}$
View full question & answer→Question 142 Marks
Find the area of an equilateral triangle each of whose sides measures: $20\ cm$ [Take $\sqrt{3}=1.73$]
AnswerEach side of equilateral triangle $(a) = 20\ cm$
$\therefore\text{Area}=\frac{\sqrt{3}}{4}\text{a}^2=\frac{\sqrt{3}}{4}\times20\times20\text{cm}^2$
$=1.73\times100=173\text{cm}^2$
View full question & answer→Question 152 Marks
Find the area of a circle whose diameter is:$ 28\ cm.$
AnswerDiameter of the circle $=28\text{cm}$
$\therefore\text{Radius}(\text{r})=\frac{28}{2}=14\text{cm}$ and
Area $=\pi\text{r}^2=\frac{22}{7}\times14\times14\text{cm}^2$
$=616\text{cm}^2$
View full question & answer→Question 162 Marks
Find the area of the square, the length of whose diagonal is: $2.4\ m.$
AnswerDiagonal of the square $= 2.4\ m$
$\therefore$ Area of the square $=\Big[\frac{1}{2}\times(\text{Diagonal})^2\Big]\text{sq. unit}$
$=\Big[\frac{1}{2}\times(2.4)^2\Big]\text{m}^2$
$=2.88\text{m}^2$
View full question & answer→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$\text { Base }=1 \mathrm{~m} 60 \mathrm{~cm}=1.6 \mathrm{~m}[\text { since } 100 \mathrm{~cm}=1 \mathrm{~m}]$
$\text { Height }=75 \mathrm{~cm}=0.75 \mathrm{~m}$
$\therefore \text { Area of the parallelogram }=\text { Base } \times \text { Height }$
$=1.6 \mathrm{~m} \times 0.75 \mathrm{~m}$
$=1.2 \mathrm{~m}^2$
View full question & answer→Question 182 Marks
Find the circumference of a circle whose diameter is:
$4.9\ m.$
AnswerDiameter of circle $(d) = 4.9\ m$
$\therefore\text{Circumference}=\text{d}\pi=\frac{4.9\times22}{7}\text{cm}$
$=7\times22=154\text{m}$
View full question & answer→Question 192 Marks
Find the area of a circle whose radius is: $3.5\ m.$
AnswerRadius of the circle $(r) =3.5\text{m}$
$\therefore\text{Area}=\pi\text{r}^2=\frac{22}{7}\times3.5\times3.5\text{m}^2$
$=38.5\text{m}^2$
View full question & answer→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.
AnswerArea 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 $=8\text{cm}$
View full question & answer→Question 212 Marks
Find the area of a rhombus in which
Each side $= 12\ cm$ and height $= 7.5\ cm.$
AnswerA 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 $=12 \mathrm{~cm} \times 7.5 \mathrm{~cm}=90 \mathrm{~cm}^2$
View full question & answer→Question 222 Marks
Find the area of a parallelogram with base $32\ cm$ and height $16.5\ cm.$
Answer$\text { Base }=32 \mathrm{~cm}$
$\text { Height }=16.5 \mathrm{~cm}$
$\therefore \text { Area of the parallelogram }=\text { Base } \times \text { Height }$
$=32 \mathrm{~cm} \times 16.5 \mathrm{~cm}$
$=528 \mathrm{~cm}^2$
View full question & answer→Question 232 Marks
Find the length of the height of an equilateral triangle of side $24\ cm.$ [Take $\sqrt{3}=1.73$] Hint $\frac{1}{2}\times24\times\text{h}=\frac{\sqrt{3}}{4}\times24\times24.$ Find h.
AnswerEach side of an equilateral triangle $= 24\ cm$
Length of altitude $=\frac{\sqrt{3}}{2}\text{a}=\frac{\sqrt{3}}{2}\times24$
$=12\sqrt{3}\text{cm}=12(1.73)=20.76\text{cm}$
View full question & answer→Question 242 Marks
Find the circumference of a circle whose diameter is: $35\ cm.$
AnswerDiameter of circle $(d) = 35\ cm$
$\therefore\text{Circumference}=\text{d}\pi=\frac{35\times22}{7}\text{cm}$
$=110\text{cm}$
View full question & answer→Question 252 Marks
Find the height of a triangle having an area of $72 \mathrm{~cm}^2$ and base 16cm.
AnswerBase of triangle $= 16\ cm$
area of the triangle = $72 \mathrm{~cm}^2$
$\therefore\text{Height}=\frac{\text{Area}\times2}{\text{Base}}$
$=\frac{72\times2}{16}$
$=9\text{cm}$
View full question & answer→Question 262 Marks
Find the area of a circle whose diameter is: $1.4\ m.$
AnswerDiameter of the circle $=1.4\text{cm}$
$\therefore\text{Radius}(\text{r})=\frac{1.4}{2}=0.7\text{cm}$
$\therefore\text{Area}=\pi\text{r}^2=\frac{22}{7}\times0.7\times0.7\text{cm}^2$
$=1.54\text{m}^2$
View full question & answer→Question 272 Marks
Find the circumference of a circle of radius $15 \ cm$. (Take $\pi = 3.14.)$
AnswerRadius of a circle $= 15\ cm$
Circumference $=2\pi\text{r}=2\times3.14\times15=94.20\text{cm}$
$=94.2\text{cm}$ View full question & answer→Question 282 Marks
Find the diameter of a circle whose circumference is $63.8\ m.$
AnswerCircumference $(c) = 63.8\ m$
$\therefore\text{Diameter}=\frac{\text{c}}{\pi}=\frac{63.8\times7}{22}\text{m}=2.9\times7$
$=20.3\text{m}$
View full question & answer→Question 292 Marks
Find the circumference of a circle whose radius is:
$1.4\ m.$
AnswerRadius of the circle $(r) = 1.4\ m$
$\therefore\text{Circumference}=2\pi\text{r}$
$=2\times\frac{22}{7}\times1.4\text{m}$
$=2\times\frac{22}{7}\times\frac{14}{10}\text{m}=\frac{44}{5}=8.8\text{m}$
View full question & answer→Question 302 Marks
Find the area of a square each of whose sides measures $8.5\ m.$
AnswerSide of square $(a)=8.5 \mathrm{~m}$
Area $=a^2=(8.5)^2=8.5 \times 8.5 \mathrm{~m}^2=72.25 \mathrm{~m}^2$
View full question & answer→Question 312 Marks
Find the area of the rectangle whose dlmensions are:
length $= 12.5m$, breadth $= 8dm.$
AnswerLength of rectangle $(\mathrm{l})=12.5 \mathrm{~m}$
Breadth $(b) =8 \mathrm{~cm}=0.80 \mathrm{~m}$
Area $=l \times b=12.5 \times 0.80 \mathrm{~m}^2=10 \mathrm{~m}^2$
View full question & answer→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$\text { Base }=14 \mathrm{dm}=(14 \times 10) \mathrm{cm}[\text { since } 1 \mathrm{dm}=10 \mathrm{~cm} \text { and } 100 \mathrm{~cm}=1 \mathrm{~m}]$
$=140 \mathrm{~cm}=1.4 \mathrm{~m}$
$\text { Height }=6.5 \mathrm{dm}=(6.5 \times 10) \mathrm{cm}$
$=65 \mathrm{~cm}=0.65 \mathrm{~m}$
$\therefore \text { Area of the parallelogram }=\text { Base } \times \text { Height }$
$=1.4 \mathrm{~m} \times 0.65 \mathrm{~m}$
$=0.91 \mathrm{~m}^2$
View full question & answer→Question 332 Marks
Find the area of a circle whose radius is: $21\ cm.$
AnswerRadius of the circle (r) $=21\text{cm}$
$\therefore\text{Area}=\pi\text{r}^2=\frac{22}{7}\times21\times21\text{cm}^2$
$=1386\text{cm}^2$
View full question & answer→Question 342 Marks
Find the area of the rectangle whose dlmensions are: length $= 24.5\ m$, breadth $= 18\ m$
AnswerLength of rectangle $(l) = 24.5\ m$ Breadth $(b) = 18\ m$
Area $=l \times b=24.5 \times 18 \mathrm{~m}^2=441 \mathrm{~m}^2$ View full question & answer→