Question

Find the area of the square whose perimeter is
(a) 32 cm
(b) 40 m
(c) 54 cm
(d) 31 m​

Answer 1

Perimeter- 4a

a) 4a=32
a=32/4
a=8

Area=side*side
8*8
64

b) 4a=40
a=40/4
a=10

Area = side*side
10*10
100

c) 4a=54
a=54/4
a=13.5

Area = side*side
13.5*13.5
182.25

d) 4a=31
a=31/4
a=7.75

Area = side*side
7.75*7.75
60.0625

Answer 2

Question:

Find the area of the square whose perimeter is

(a) 32 cm

(b) 40 m

(c) 54 cm

(d) 31 m

To find :

• In each case we have to find Area of square .

Given:

• In each case value of Perimeter is given

Formula used:

• $\sf \: perimeter = 4 \times side$
• $\sf{ Area = {side}^{2} }$

Answer:

Part 1:

$\bf{ \star \: we \: know : }$

$\sf \: perimeter = 4 \times side$

By using this formula we can find length of side

$: \implies\sf \: 32 = 4 \times side$

$: \implies\sf \: side = \dfrac{ { \cancel{32}}^{ \: 8} }{ { \cancel{4}}^{ \: 1} }$

$: \implies \blue{ \sf side = 8cm}$

Now we can find area by using this formula:

$\sf{Area = side\times side} \: \: \: \: \: \: or \ \: \: \: \: \: Area = {side}^{2}$

$: \implies \sf \: Area = {8}^{2}$

$: \implies \star \boxed{{ \sf \: Area = 64 {cm}^{2} }} \star$

Part 2:

$\bf{ \star \: we \: know : }$

$\sf \: perimeter = 4 \times side$

By using this formula we can find length of side

$: \implies\sf \: 40= 4 \times side$

$: \implies\sf \: side = \dfrac{ { \cancel{40}}^{ \: 10} }{ { \cancel{4}}^{ \: 1} }$

$: \implies \blue{ \sf side = 10m}$

Now we can find area by using this formula:

$\sf{Area = side\times side} \: \: \: \: \: \: or \ \: \: \: \: \: Area = {side}^{2}$

$: \implies \sf \: Area = {10}^{2}$

$: \implies \star \boxed{{ \sf \: Area = 64 {m}^{2} }} \star$

Part 3:

$\bf{ \star \: we \: know : }$

$\sf \: perimeter = 4 \times side$

By using this formula we can find length of side

$: \implies\sf \: 54= 4 \times side$

$: \implies\sf \: side = \dfrac{ { \cancel{54}}^{ \: 13.5} }{ { \cancel{4}}^{ \: 1} }$

$: \implies \blue{ \sf side = 13.5cm}$

Now we can find area by using this formula:

$\sf{Area = side\times side} \: \: \: \: \: \: or \ \: \: \: \: \: Area = {side}^{2}$

$: \implies \sf \: Area = {13.5}^{2}$

$: \implies \star \boxed{{ \sf \: Area = 182.25{cm}^{2} }} \star$

Part 4:

$\bf{ \star \: we \: know : }$

$\sf \: perimeter = 4 \times side$

By using this formula we can find length of side

$: \implies\sf \: 31= 4 \times side$

$: \implies\sf \: side = \dfrac{ { \cancel{31}}^{ \:7.75 } }{ { \cancel{4}}^{ \: 1} }$

$: \implies \blue{ \sf side = 7.75m}$

Now we can find area by using this formula:

$\sf{Area = side\times side} \: \: \: \: \: \: or \ \: \: \: \: \: Area = {side}^{2}$

$: \implies \sf \: Area = {7.75}^{2}$

$: \implies \star \boxed{{ \sf \: Area = 60.06{m}^{2} }} \star$

A Small Advice:

Beware of units. eg here in 1 part perimeter is given in cm so answer i.e. area should also be in cm and in 2 part perimeter is given in m so answer i.e. area should also be in m. ;)

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And all we are done!✔

:D