Question

Short Answer Type Questions :-

1. Area of a square is 144 cm². Find its perimeter.

2. Perimeter of a square is 320 m. Find its area.

3. Find the area of annulus, whose inner and outer radii are 15 cm and 18 cm respectively.

4. Perimeter of a rectangle is 30 cm. If its length is 9 cm, find its area.

5. Circumference of a circle is 88 cm. Find its area.

6. Area of a circle is 1386 cm². Find its circumference.
$\sf( Use \: \pi = \frac{22}{7} )$

7. The area of a rectangular field is 750 m². If the length of the field is 30 m, what is its breadth? Also find the perimeter of the rectangular field.

8. A rectangular park is 65 m and 40 m wide. A path 3.5 m wide is constructed outside the park. Find the area of the path.​

Answer 1

Answers:

1. Formula for area of a square = a²

Given area = 144 cm²

a² = 144 cm²

So, a = √144

a = 12 cm

Perimeter = 4a

= 4 x 12 = 48 cm

2. Formula for perimeter = 4a

Given perimeter = 320 m

4a = 320 m

a = 320/4 = 80 m

Formula for area = a²

= 80 x 80 = 6400 m²

3. Inner radius [r] = 15 cm

Outer radius [R] = 18 cm

Formula for Area = π(R² - r²)

It can be written as π(R+r) (R-r)

$\sf{=3.14\times(18-15)(18+15)}$

$\sf{3.14\times3\times33}$

= 310.86 cm²

4. Formula to find perimeter = 2 (l + b)

Perimeter = 30 cm

Length = 9 cm

2 (9 + b) = 30 cm

18 + 2b =30 cm

2b = 30 - 18 = 12

b = 12/2 = 6 cm

Area = lb

= 9 x 6 = 54 cm²

5. Formula to find circumference = 2πr

Circumference = 88 cm

$\sf{2\times\dfrac{22}{7}\times\:r=88\:cm}$

$\sf{\dfrac{44}{7}\times\:r=88\:cm}$

$\sf{r=88\times\dfrac{7}{44}}$

$\sf{r=14\:cm}$

Radius = 14 cm

Area = πr²

$\sf{\dfrac{22}{7}\times14\times14}$

= 616 cm²

6. Formula to find area = πr²

Area = 1386 cm²

$\sf{\dfrac{22}{7}\times\:r\times\:r=1386\:cm^2}$

$\sf{r^2=1386\times\dfrac{7}{22}}$

$\sf{r^2=63\times7}$

$\sf{r^2=441}$

So, r = √441 = 21 cm

Circumference = 2πr

$\sf{2\times\dfrac{22}{7}\times21}$

= 132 cm

7. Formula for area of a rectangle = lb

Area = 750 m²

Length = 30 m

30 x b = 750

b = 750/30

b = 25 m

Perimeter of a rectangle = 2 (l + b)

= 2 x (30 + 25)

= 2 x 55

= 110 m

8. Area of path = Area of total park - Area of actual park

Area of path = [(65+3.5+3.5) x (40+3.5+3.5)] - (65 x 40)

= [72 x 47] - 2600

= 3384 - 2600

= 784 m²

★ Final Answers:

1. 48 cm

2. 6400 m²

3. 310.86 cm²

4. 54 cm²

5. 616 cm²

6. 132 cm

7. 25m, 110 m

8. 784 m²

Answer 2

Answer:

$\huge \sf \purple{ \underline{ \underline{Question 1.}}}$

Area of a square is 144 cm². Find its perimeter.

$\huge \bf{ \underline{ \underline{Solution:- }}}$

• Area of square= 144cm²
• To find the perimeter we will first find the side of square.

$\sf \: Area \: of \: square = {side}^{2}$

$\sf \: {side}^{2} = 144cm$

$\sf \: side = \sqrt{144} = 12cm$

Therefore the side of square is 12 cm.

• Perimeter of square=4× side

$\sf perimeter \: of \: rectangle = 4 \times 12cm$

$\sf = 48cm$

$\sf \therefore \: the \: perimeter \: of \: square \: is \: 48 \: cm$

$\huge \sf \red{ \underline{ \underline{Question 2.}}}$

Perimeter of a square is 320 m. Find its area.

Solution:-

• Perimeter of square is 320 m.
• to find its area we will find its sides.

Perimeter of square = 4 ×side

4 × side = 320m

side = 320/4 = 80cm

Therefore the side of square is 80 cm.

• Area of square= side×side

area of square = side × side

= 80cm × 80cm

= 6400 cm²

$\huge \sf\pink{ \underline{ \underline{Question 3.}}}$

Find the area of annulus, whose inner and outer radii are 15 cm and 18 cm respectively.

Solution:-

Inner radius, r = 15 cm

Outer radius, R = 18 cm

Area of circular ring

= π(R+r)(R-r)

= 3.14(18-15)(18+15)

= 3.14×3×33

= 310.86 cm²

$\huge \sf{ \color{maroon}{ \underline{ \underline{Question 4.}}}}$

Perimeter of a rectangle is 30 cm. If its length is 9 cm, find its area.

$\huge \bf{ \underline{ \underline{Solution:- }}}$

• Perimeter of rectangle 30 cm.
• Length of rectangle 9 cm
• To find its area.

$\sf \: Perimeter \: of \: rectangle = 2 \times (l + b)$

$\sf = 2(9 + \: b) = 30cm$

$\sf = 9 + b = \frac{30}{2} cm$

$\sf = 9 + b = 15cm$

$\sf \: b = 15 - 9 = 6cm$

• Therefore the breadth is 6cm.

Now, we will find the area of rectangle.

$\sf \: Area \: of \: rectangle = 9 \times 6 = 54cm$

$\sf \therefore \: the \: area \: is \: 54cm$

$\huge \sf{ \color{goldenrod}{ \underline{ \underline{Question 5.}}}}$

Circumference of a circle is 88 cm. Find its area.

$\huge \bf{ \underline{ \underline{Solution:- }}}$

$\sf \: Circumference = 2\pi \: r$

$\sf88 = r$

$\sf \: r = \frac{44 \times 7}{22}$

$\sf \: r \implies 14cm$

$\sf \: area = \pi {r}^{2}$

$\sf = \pi \times 14m \times 14 {m}$

$\sf = 196\pi \: cm {}^{2}$

$\huge \sf{ \color{aqua}{ \underline{ \underline{Question 6.}}}}$

Area of a circle is 1386 cm². Find its circumference.

$\huge \bf{ \underline{ \underline{Solution:- }}}$

• Given,
• that area = 1386 cm²

$\sf \: Area \: of \: circle = πr²$

$\sf \: so,∴ πr² = 1386$

$\sf \: r² = 1386× \frac{22}{7}$

$\sf \: r {}^{2} = \sqrt{441} cm$

$\sf∴  r = 21 cm$

$\sf \: Circumference \: of \: the \: field= 2πr$

$\sf = 2 \times   \frac{22}{7} \times 21 = 132cm.$

$\huge \sf{ \color{lime}{ \underline{ \underline{Question 7.}}}}$

The area of a rectangular field is 750 m². If the length of the field is 30 m, what is its breadth? Also find the perimeter of the rectangular field.

$\huge \bf{ \underline{ \underline{Solution:- }}}$

• Let the breadth of the rectangular field be x
• Then, length of the field = x + 30

According to question,

Perimeter = 640

And we know that perimeter of rectangle is 2( length + breadth)

Using this formula,

$\sf2( l + b ) = 640$

$\sf2( x + 30 + x ) = 640$

$\sf2x + 30 = \frac{640}{2}$

$\sf2x = 320- 30$

$\sf \: x = \frac{290}{2} = 145x$

Therefore, Length of field = x + 30 = 145 + 30 = 175.

$\huge \sf{ \color{orange}{ \underline{ \underline{Question 8.}}}}$

A rectangular park is 65 m and 40 m wide. A path 3.5 m wide is constructed outside the park. Find the area of the path.

$\huge \bf{ \underline{ \underline{Solution:- }}}$

area of path is  area of park with path - area of rectangular park                      

$\sf \: area \: of \: park =l x b$

$\sf= 45 x 30=1350 cm {}^{2}$

$\sf \: area \: of \: park \: with \: path \: is =45+2.5+2.5 x 30+2.5+2.5$

$\sf = 1750cm {}^{2}$

$\sf \: area \: of \: path = 1750-1350=400 cm {}^{2}$