Question

Question:−
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The perimeter of a trapezium is 116m,it's non parallel sides are 16m and 24m and it's altitude is 16m. find the area of the trapezium.​
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Note : Step by step Explanation & Diagram required!
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Answer 1

Answer:

its perimeter of trapezam is 116 parallel sides are 24 inyo 16

Answer 2

Given :

• Perimeter of the Trapezium = 116 m

• Non-Parallel Sides = 16 m and 24 m

• Altitude = 16 m

To Find :

• Area of the Trapezium

Solution :

Let the parallel sides be a and b

$\bigstar\boxed{ \purple{ \sf \: Perimeter \: = Sum \: of \: all \: sides }}★ </p><p>$

$\longrightarrow \sf \: 116 = 16 + 24 + a + b$

$\longrightarrow \sf \: 116 = 40 + a + b$

$\longrightarrow \sf \:a + b = 116 - 40$

$\longrightarrow \sf \:a + b = 76$

Hence,Sum of Parallel Sides = 76 m

Now, Let's Find Area of the Trapezium :

$\bigstar\boxed{ \purple{ \sf \: Area \: of \: Trapezium = \dfrac{1}{2} (a + b) \times h}}★$

$\longrightarrow \sf \: \dfrac{1}{2} (76) \times 16$

$\longrightarrow \sf \: \dfrac{1}{2} \times 76 \times 16$

$\longrightarrow \sf \cancel \dfrac{1216}{2}$

$\longrightarrow \sf \red{ {608 \: m}^{2} }</p><p>$

Hence,Area of the Trapezium is 608 m^2