Math Mensuration Made Great : With Word Problem For Class 8th,9th,10th[13]

Q.1) The parallel sides of a trapezium having area1 120cm² are in the ratio 3 : 5. If the distance between the parallel sides is 10cm, find the measures of the parallel sides of the trapezium.

SOLUTION :

Given:
Let the measures of the parallel sides of the trapezium be 3x and 5x.
Then area of the trapezium = 120cm²

1 / 2 ( sum of the parallel sides ) * height = 120cm²
1 / 2 ( 3x + 5x ) * 10cm = 120cm²
( 40x ) cm = 120cm²
x = 120 / 40cm = 3cm
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Q.2) The area of a rhombus is 300 sq m. If one of its diagonal is 30m , find the other diagonal.

SOLUTION:

Given:
Area of the rhombus = 300m²
1 / 2 * d₁ * d₂ = 300m²
1 / 2 * 30m * d₂ = 300m²
d₂ = 300 / 30 * 2 / 30 = 20m
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Q.3) The diagonals of a rhombus are 12cm and 5cm. Find its (a) area and (b) side.

SOLUTION:

Given:
(a) Let d₁ = 12cm and d₂ = 5cm be the diagonals of the given rhombus

Then area of the rhombus = 1 / 2 * d₁ * d₂
= 1 / 2 * 12cm * 5cm = 30 sq cm

(b) Side of the rhombus = 1 / 2 √d₁² + √d₂²
= 1 / 2 √12² + √5² cm
= 1 / 2 √144 + √25 cm
= 1 / 2 √ 169 cm = 13 / 2 cm = 6.5cm
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