Question

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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Answer 1

Given :

• Perimeter of the trapezium = 116 m

• Non parallel sides are 16 m and 24 m

• Altitude = 16 m

To Find :

• Area of the Trapezium

Solution :

Let the parallel sides of the trapezium be x and y

We know that,

$\bigstar \: \boxed{ \sf \: Perimeter = Sum \: of \: all \: sides}$

$\longrightarrow \sf \: 116 = 16 + 24 + x + y$

$\longrightarrow \sf \: 116 =40 + x + y$

$\longrightarrow \sf \: 116 - 40 = x + y$

$\longrightarrow \sf \: 76= x + y$

$\longrightarrow \red{\sf \:x + y = 76}$

Sum of parallel sides is 76 m

Let's find area now :

$\bigstar \: \boxed{ \sf \: Area_ {Trapezium }= \dfrac{1}{2} \times Sum \: of \: parallel\: sides \times height}$

$\longrightarrow \sf \: Area = \: \dfrac{1}{2} \times (x + y) \times h$

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

$\longrightarrow \sf \: Area = \cancel \dfrac{1216}{2}$

$\longrightarrow \sf \red{ \sf \:Area = 608 {m}^{2} }$

$\therefore$ Area of the trapezium is 608 m²

Answer 2

Answer:

Refer to the diagram attached.

Given that:-

• AD = 16m (Non parallel side - 1)
• BC = 24m (Non parallel side - 2)
• BE = 16m (Altitudes)
• Perimeter = 116m

To Find:-

• Area of Trapezium

Solution:-

Here, Perimeter = 116m

Two sides given are 16m and 24m.

Hence, x + y + 16 + 24 = 116

x + y = 116 - (40)

x + y = 76 m

Hence, the sum of parallels = 76 m.

Area of Trapezium = ½ * Sum of parallels * altitude

Area = ½ * 76 * 116

Area = 38 * 116

Area = 608 m²