Perimeter and Area Test

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Perimeter and Area Test - 28

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Weekly Quiz Competition

Question 1
1 / -0

Find the area of a parallelogram with a base of $$200$$ cm and height of $$2.5$$ cm.

A
$$500$$ $$cm^{2}$$

B
$$510$$ $$cm^{2}$$

C
$$520$$ $$cm^{2}$$

D
$$300$$ $$cm^{2}$$

Solution

Area of a parallelogram $$=$$ base $$\times$$ height
$$=200 \times 2.5$$
$$= 500$$ $$cm^{2}$$
Question 2
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Find the base of parallelogram if its area is $$\displaystyle 80{ cm }^{ 2 }$$ and altitude is $$10$$ cm.

A
$$6$$ cm

B
$$8$$ cm

C
$$10$$ cm

D
None of the above

Solution

Given, area of parallelogram $$=80\ cm^2$$
Altitude, $$a=10\ cm$$
Let, the base be $$b$$

For a parallelogram,
$$Area=Base\times Altitude$$
$$\Rightarrow 80=b\times 10$$
$$\Rightarrow b=\dfrac{80}{10}$$
$$\Rightarrow b=8$$

Hence, the base of the parallelogram is $$8\ cm$$
Question 3
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A parallelogram has an area of $$125$$ $$m^{2}$$ and a height of $$5\ m.$$ Find the base.

A
$$250$$ m

B
$$25$$ m

C
$$270$$ m

D
$$28$$ m

Solution

Area of a parallelogram$$=base\times height$$. Let the base be 'b'.
Hence
$$125m^{2}=5b$$ or $$b=25m$$
Therefore $$base=25m$$.
Question 4
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A circular lawn with a radius of $$5$$ meters is surrounded by a circular walkway that is $$4$$ meters wide (see figure). What is the area of the walkway?

A
$$48\ \pi \ m^2$$.

B
$$60\ \pi \ m^2$$.

C
$$56\ \pi \ m^2$$.

D
$$42\ \pi \ m^2$$.

Solution

The area of the walkway is the area of the entire image (walkway + lawn) minus the area of the lawn. To find the area of each circle, use the formula:
Large circle: $$A = \pi r^2 = \pi (9)^2 = 81\pi$$
Small circle: $$A = \pi r^2 = \pi(5)^2 =25\pi$$
Thus, required area = $$81\pi-25\pi= 56\pi m^2$$.
Question 5
1 / -0

Find the area of a parallelogram with a base of $$34$$ meters and a height of $$8$$ meters.

A
262 $$m^{2}$$

B
272 $$m^{2}$$

C
282 $$m^{2}$$

D
292 $$m^{2}$$

Solution

Area of a parallelogram = base $$\times$$ height
= $$34 \times 8$$
= $$272$$ $$m^{2}$$
Question 6
1 / -0

A parallelogram has an area of $$60$$ $$cm^{2}$$ and a base of $$12cm$$. Find the height.

A
$$3$$ cm

B
$$4$$ cm

C
$$5$$ cm

D
$$6$$ cm

Solution

Area of a parallelogram = base $$\times$$ height
$$60 = 12 \times height$$
height $$=60 \div 12$$
height $$=5$$ $$cm$$
Question 7
1 / -0

Calculate the area of a parallelogram with a base of $$ 12$$ m and height of $$5$$ m.

A
59 $$m^{2}$$

B
60 $$m^{2}$$

C
61 $$m^{2}$$

D
62 $$m^{2}$$

Solution

Area of a parallelogram = base $$\times$$ height
= $$12 \times 5$$
= $$60$$ $$m^{2}$$
Question 8
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Find the area and inner circumference of the ring.

A
$$9.48$$ sq. cm, $$3.14$$ cm

B
$$9.42$$ sq. cm, $$6.48$$ cm

C
$$9.42$$ sq. cm, $$2.14$$ cm

D
None of these

Solution

Area of a circular ring = $$\pi(R^2-r^2)$$
$$=$$ $$3.14(2^2-1^2)$$
$$= 3.14 \times 3$$
$$= 9.42$$ sq. cm
Inner circumference $$=$$ $$2\pi r$$
$$= 2 \times 3.14 \times 1$$
$$= 6.28$$ cm
Question 9
1 / -0

Find the perimeter of the figure outlined by solid line in terms of $$x$$.

A
$$5x+3\pi x$$

B
$$5x+6\pi x$$

C
$$10x+3\pi x$$

D
$$10x+6\pi x$$

Solution

Perimeter of the figure $$=$$ Length of slanting sides of triangle + Circumference of semicircle
Circumference of semicircle $$=\pi r = \dfrac {22}{7} \times 3x = \dfrac {66x}{7}= 3 \pi x$$
For the two right angle triangle,
By Pythagoras theorem
$$(Hyp)^2 = (4x)^2+ \left(\dfrac{6x}{2}\right)^2$$
$$=16x^2+9x^2$$
$$=25x^2$$
Hyp $$= 5x$$ units
Length of two slanting sides of triangle $$=2 \times 5x = 10x$$
Perimeter of the figure $$=(3 \pi x + 10x)$$ units
Question 10
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Sonali pounded a stake into the ground, when she attached a rope to both the stake and her dog's collar, the dog could reach $$9$$ feet from the stake in any direction. Find the approximate area of the lawn, in square feet, the dog could reach from the stake. ( $$\displaystyle \pi $$ =3.14)

A
$$28$$

B
$$57$$

C
$$113$$

D
$$254$$

Solution

Dog can reach $$9$$ feet from the stake in any direction, so radius of the circular ground will be $$9$$.
We know formula for area of circle is $$\pi { r }^{ 2 }$$
Hence area will be $$3.14\times { 9 }^{ 2 }$$(value of pi is given)
$$=3.14\times 81=254.34$$

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Perimeter and Area Test - 28

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Perimeter and Area Test - 28

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SHARING IS CARING

Question 1

$$500$$ $$cm^{2}$$

$$510$$ $$cm^{2}$$

$$520$$ $$cm^{2}$$

$$300$$ $$cm^{2}$$

Solution

Question 2

$$6$$ cm

$$8$$ cm

$$10$$ cm

None of the above

Solution

Question 3

$$250$$ m

$$25$$ m

$$270$$ m

$$28$$ m

Solution

Question 4

$$48\ \pi \ m^2$$.

$$60\ \pi \ m^2$$.

$$56\ \pi \ m^2$$.

$$42\ \pi \ m^2$$.

Solution

Question 5

262 $$m^{2}$$

272 $$m^{2}$$

282 $$m^{2}$$

292 $$m^{2}$$

Solution

Question 6

$$3$$ cm

$$4$$ cm

$$5$$ cm

$$6$$ cm

Solution

Question 7

59 $$m^{2}$$

60 $$m^{2}$$

61 $$m^{2}$$

62 $$m^{2}$$

Solution

Question 8

$$9.48$$ sq. cm, $$3.14$$ cm

$$9.42$$ sq. cm, $$6.48$$ cm

$$9.42$$ sq. cm, $$2.14$$ cm

None of these

Solution

Question 9

$$5x+3\pi x$$

$$5x+6\pi x$$

$$10x+3\pi x$$

$$10x+6\pi x$$

Solution

Question 10

$$28$$

$$57$$

$$113$$

$$254$$

Solution

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