Question

The perimeter of a trapezium is 152m, its non-parallel sides are 18m and
24m and its altitude is 12m. Find the area of trapezium.​

Answer 1

Given :

• Perimeter of a trapezium is 152 m
• Non-parallel sides of a trapezium are 18 m and 24 m
• Height of a trapezium = 12 m

To Find :

• Area of trapezium.

Calculations :

Firstly let's calculate the length of non-parallel sides of a trapezium,

$\mapsto \sf 18 + 24 \: m$

On adding the numbers,

$\mapsto \rm{ \green{42 \: m}}$

• So, length of non-parallel sides of a trapezium is 42 m.

Now, let's calculate the length of non-parallel sides, so in order to calculate non-parallel sides, we need to perform subtraction in :-

• Perimeter of trapezium (152 m) - total length of parallel sides (42 m)

So, let's find the length parallel sides of a trapezium,

$\mapsto \sf 152 \: m - 42 \: m$

On subtracting the numbers,

$\mapsto \rm{ \green{110 \: m}}$

• So, the length of parallel sides of a trapezium is 110 m.

According to the Question,

Now, let's calculate the area of trapezium, In order to find the area of trapezium,

Formula to be used :

• $\boxed{\rm{ \pink{{Area_{(Trapezium)} = \dfrac{1}{2} \times Sum \: of \: parallel \: sides \times height}}}}$

$\dag$ Putting the values,

$\mapsto \sf Area_{(Trapezium)} = \dfrac{1}{2} \times 110 \: m \times 12 \: m \\ \\ \mapsto \sf Area_{(Trapezium)} = 55 \: m \times 12 \: m \\ \\ \mapsto \sf \boxed{ \bf{Area_{(Trapezium)} = 660 \: m^2 }} \: \pink{\bigstar}$

Henceforth,

• Area of trapezium is 660 m².

Answer 2

★ Given :

The perimeter of a trapezium is 152m, its non-parallel sides are 18m and 24m and its altitude is 12m.

★ To find :

Find the area of trapezium.

★ Solution :

⚘Length of non Parrallel sides

➞ 18 + 24

➞ 42 cm

⚘Length of Parrallel sides

➞ 152 - 42

➞ 110 m

⚘We know that, Area of trapezium

➞ 1/2 × Sum of Parrallel sides × H

➞ 1/2 × ( 110 ) × 12

➞ 1/2 × 1320

➞ 660 m²

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