Question

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Answer 1

Question 1

The area of a parallelogram is 60cm^2 and one of it's altitude is 5cm. The length of the corresponding side is?

Solution :-

Area of parallelogram = l x b

Here,

• l = 5cm
• area = 60cm^2
• b = ?

substituting values in the formula,

area = l x b

60 = 5 x b

60 = 5b

60/5 = b

12 = b

•°• Length of corresponding side is 12cm

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Question 2

If the diagonals of a rhombus gets doubled, then the area of the rhombus becomes ----- it's original area.

Solution :-

Original Area of rhombus = 1/2(d x d')

Here,

• d and d' are the two diagonals.

Now, when we double the diagonals, it becomes

2d and 2d'

and area becomes,

1/2(2d x 2d')

= 1/2(4dd')

= 2dd'

Comparing original area and new area,

$\rightarrow \frac{2dd'}{ \frac{1}{2}(d \times d') } \\ \rightarrow \: \frac{2dd'}{1} \times \frac{2}{1} (d \times d') \\ \rightarrow 4dd'$

•°• The area becomes 4 times the original area.

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Question 3 :-

If the diagonal d of a quadrilateral is doubled and the heights h and h' falling on d are halved, then the area of the quadrilateral is?

Solution :-

Let the quadrilateral be ABCD.

Here,

• AD be height 1 (h)
• BC be height 2 (h')
• AC be the diagonal (d)

Area = 1/2( h + h')d

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Question 4 :-

Area of a traingle is 60cm^2 and altitude is 24cm, then it's corresponding base-?

Solution :-

Area of triangle = 1/2 x b x h

60 = 1/2 x b x 24

60 x 2 = 24b

120 = 24b

b = 120/24

b = 5

•°• length of corresponding base is 5cm

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Question 5 :-

Area of square whose side is 25cm -?

Solution :-

Area of square = s^2

Here,

• s = 25

Area = 25 x 25

•°• Area = 625cm^2

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Question 6 :-

Length of a rectangle whose area is 280cm^2 is 20cm, then breadth is -?

Solution :-

Area of rectangle = 2(l+b)

280 = 2(20 + b)

280 = 40 + 2b

240 = 2b

b = 240/2

b = 120cm

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Question 7 :-

The length of parallel sides of a trapezium are in the ratio 2:3. The distance between parallel sides and its area are 12m and 300m^2 . The lenght of parallel sides are -?

Solution :-

Area of trapezium = 1/2(d1 + d2)h

Here,

• Let the parallel sides be 2x and 3x
• h = 12

300 = 1/2( 2x + 3x ) 12

600 = 5x(12)

600 = 60x

x = 600/60

x = 10

Length of parallel sides,

2x = 2(10) = 20m

3x = 3(10) = 30m

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