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

2 thoughts on “The perimeter of a trapezium is 152m, its non-parallel sides are 18m and<br />24m and its altitude is 12m. Find the area of trapez”

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,

   [tex] \mapsto \sf 18 + 24 \: m [/tex]

   On adding the numbers,

   [tex] \mapsto \rm{ \green{42 \: m}} [/tex]

   • 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,

   [tex] \mapsto \sf 152 \: m – 42 \: m [/tex]

   On subtracting the numbers,

   [tex] \mapsto \rm{ \green{110 \: m}} [/tex]

   • 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 :

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

   [tex] \dag [/tex] Putting the values,

   [tex] \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} [/tex]

   Henceforth,

   • Area of trapezium is 660 m².

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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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