Question

Area of a Trapezium is 324 m

2.One of the parallel sides is 14 m

longer than the other and height is 18 m. Find its two parallel sides I'M WEAK IN MATHS PLEASEEE HELP​

Answer 1

Question :-

The area of a trapezium is 324m² One of the parallel sides is 14m longer than the other and the height is 18m. Find the parallel sides.

Given :-

• Area of a trapezium = 324cm²
• Height = 18cm

Aim :-

• To find the parallel sides of the trapezium.

According to the question,

Let one parallel side be = x

Second parallel side = x + 14

Formula :-

The Area of a trapezium is :-

$Area \: of \: a \: trapezium = \dfrac{1}{2} \times height \times (sum \: of \: parallel \: sides)$

Substituting the values, we get :-

$324 = \dfrac{1}{2} \times 18 \times (x + x + 14)$

Adding the terms inside the brackets,

$= > 324 = \dfrac{1}{2} \times 18 \times (2x + 14)$

By cancelling,

$324 = \dfrac{1}{ \cancel2} \times \cancel{18} \times (2x + 14)$

$324 = 9 \times (2x + 14)$

By transposing 9 to the LHS (Left Hand Side),

$\dfrac{324}{9} = 2x + 14$

Reducing to the lowest terms,

$36 = 2x + 14$

Transposing 14 to the LHS (Left Hand side),

$36 - 14 = 2x$

$22 = 2x$

Transposing 2,

$\dfrac{22}{2} = x$

Reducing to the lowest terms,

$11 = x$

Hence,

• x = 11
• x + 14 = 25

The two parallel sides of the trapezium are 11m and 25m.

Verification :-

Substituting x and x + 14 as 11m and 25m respectively in the equation, let us verify the answer.

$324 = \dfrac{1}{2} \times 18 \times (11 + 25)$

By cancellation,

$324 = 9 \times (36)$

When multipled the product is the same.

therefore,

LHS = RHS

HENCE VERIFIED

Some more formulas :-

• Area of a triangle = ½ × Base × Height
• Area of a square = (side)²
• Area of a rectangle = Length × Breadth
• Area of a parallelogram = Base × Height
• Area of a rhombus = ½ × Base × Height