Area and perimeter Questions and answers

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Elementary Mathematics

31). What is the area of a square having perimeter 68 cm?

A). 361 sq cm

B). 284 sq cm

C). 269 sq cm

D). 289 sq cm

View Answer

32). The diagonal of a square is \( \Large \Large 4\sqrt{2} \) cm. The diagonal of another square whose area is double that of the first square is

A). 8 cm

B). \( \Large 8\sqrt{2} \)cm

C). \( \Large 4\sqrt{2} \)cm

D). 6 cm

View Answer

Correct Answer: 8 cm

Diagonal of square = \( \Large \sqrt{2} a \) [a = side] .

\( \Large 4\sqrt{2} \)=\( \Large \sqrt{2} a \)

a = 4 cm

Now, area of square = \( \Large a^{2} \)=\( \Large (4)^{2} \)=16

Side of a square whose area is \( \Large 2\times 16 \)

\( \Large a^{2}_{1} \)=32 => \( \Large a_{1}=\sqrt{32} \) => \( \Large a_{1}= 4\sqrt{2} \)

Now, diagonal of new square

= \( \Large \sqrt{2} a \)=\( \Large \sqrt{2}\times 4\sqrt{2} \)=8 cm

33). If the sides of a square is increased by 25%, then the area of the square will be increased by

A). 125%

B). 50%

C). 56.25%

D). 53.75%

View Answer

34). The perimeter of two squares is 12 cm and 24 cm. The area of the bigger square is how many times that of the Smaller?

A). 2 times

B). 3 times

C). 4 times

D). 5 times

View Answer

Correct Answer: 4 times

We know that,

Perimeter of square = \( \Large 4\times Side \)

= \( \Large 4\times a \) = 12

=> a = 3

Area of smaller square

= \( \Large 3\times 3=9 cm^{2} \) ...(i)

Now, \( \Large 4\times b \) = 24

=> b = 6

Area of bigger square

= \( \Large 6\times 6=36 cm^{2}=4\times 9 cm^{2} \)

= \( \Large 4\times Area \) of smaller square [from Eq. (ii]

Heance area of bigger square is 4 times that of smaller square

35). The perimeters of two squares are 68 cm and 60 cm. Find the perimeter of the third Square whose area is equal to the difference of the areas of these two squares.

A). 64 cm

B). 60 cm

C). 32 cm

D). 8 cm

View Answer

Correct Answer: 32 cm

\( \Large a_{1} \)=\( \Large \frac{68}{4} \)=17cm

and \( \Large a_{2} \)=\( \Large \frac{60}{4} \)=15cm

According to the question,

Area of the third square

= [\( \Large (17)^{2}-(15)^{2} \)]

= (17 + 15) (17 - 15)

= \( \Large 32\times 2 \)

= 64 sq cm

Let \( \Large a_{3} \) = Side of the third square

According to the question.

\( \Large (a_{3})^{2} \) = 64 sq cm

\( \Large a_{3} \) = \( \Large \sqrt{64} \) = 8 cm

Perimeter of the third square

= \( \Large 4\times a_{3}=4\times 8 \)=32cm

36). In the figure, side of each square is 1 cm. The area, in sq cm of the shaded part is

A). 8

B). 9

C). 10

D). 11

View Answer

Correct Answer: 10

Shaded part ABCD can be visualised as \( \Large \triangle ABD \) + \( \Large \triangle BCD \)

{where BD is common base and AB and CE are respective heights}

so, area can be calculated by finding the area of two triangles and adding them.

Area of shaded region

= Area of \( \Large \triangle ABD \) + Area of \( \Large \triangle BCD \)

=\( \Large \frac{1}{2}AB\times BD+\frac{1}{2}CE\times BD \)

= \( \Large \frac{1}{2}\times 3\times 4+\frac{1}{2}\times 2\times 4 \)=6+4

= 10 sq cm

37). Diagonals of a rhombus are 1 m and 1.5 m in lengths. The area of the rhombus is

A). \( \Large 0.75 m^{2} \)

B). \( \Large 1.5 m^{2} \)

C). \( \Large 1.5 m^{2} \)

D). \( \Large 0.375 m^{2} \)

View Answer

38). If the diagonals of a rhombus are 4.8 cm and 1.4 cm, then what is the perimeter of the rhombus?

A). 5 cm

B). 10 cm

C). 12 cm

D). 20 cm

View Answer

39). Angles of a quadrilateral are in the ratio 3: 4: 5: 8. The smallest angle is

A). 54 degree

B). 40 degree

C). 36 degree

D). 18 degree

View Answer

Correct Answer: 54 degree

Let First angle = 3x

Second angle = 4x

Third angle = 5x

and fourth angle = 8x

We know 3x + 4x+ 5x + 8x = 360 degree

=> 20x = 360 degree

x = 18 degree

Measure of smallest angle

= 3x =\( \Large 3\times 18 \ degree \)=54 degree

40). Find the distance between the two parallel sides of a trapezium if the area of the trapezium is 500 sq m and the two parallel sides are equal to 30 m and 20 m, respectively.

A). 20 cm

B). 15 cm

C). 18 cm

D). 25 cm

View Answer

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