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.​

Answer 1

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

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

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

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

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

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

Hence,Sum of Parallel Sides = 76 m

Now, Let's Find Area of the Trapezium :

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

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

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

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

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

Hence,Area of the Trapezium is 608 m^2

Answer 2

Given :

• The perimeter of a trapezium is 116 m
• It's non parallel sides are 16 m and 24 m.
• Altitude = 16 m.

To Find :

• Area of the trapezium.

Solution :

Perimeter as we know is the sum of all sides.

We have, perimeter = 116 m.

Let the two parallel sides be x and y.

- One non parallel side = 16 m

-Other non parallel side = 24 m

-Altitude of the trapezium → 16 m

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

$\longrightarrow$ $\sf{116=x+y+30}$

$\longrightarrow$ $\sf{116-30=x+y}$

$\longrightarrow$ $\sf{76=x+y \:\:....(i)}$

x and y are the parallel sides of the trapezium.

And from equation (i), we have sum of x and y equals as 76.

Which gives us the quantity sum of parallel sides in the formula of area of trapezium.

Let's use the formula of area of trapezium

$\large{\boxed{\sf{\purple{Area\:of\:trapezium\:=\:\dfrac{1}{2}\:\times\:(sum\:of\:parallel\:sides)\:\times\:height}}}}$

Block in the data,

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

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

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

$\longrightarrow$ $\sf{Area\:=\:608}$

$\large{\boxed{\sf{\red{Area\:of\:trapezium\:=\:608\:m^2}}}}$