Question

The area of a trapezium is 1080 sq cm. If the lengths of its parallel sides are 50 cm and 40 cm, find the distance between them. ​

Answer 1

Step-by-step explanation:

Area of Trapezium => 1080

$\frac{1}{2} \times sum \: of \: parallel \: sides \: \times h$

$\frac{1}{2} \times 50 + 40 \times h = 1080$

45 x h = 1080

h =

$\frac{1080}{45}$

=> 25 cm height

Answer 2

Given :-

Area of the trapezium = 1080 cm²

length of 1st parallel side = 50 cm

length of 2nd parallel side = 40 cm

To Find :-

The height of the trapezium

Solution :-

Let the height of the trapezium be h cm

We know that,

Area of a trapezium = 1/2 × (sum of parallel sides) × height

On inserting the values in the formula

We get ,

${\sf{Area\: of\: trapezium\: =\: {\dfrac{1}{2}}\: \times\: (50\: +\: 40)\: \times\: h}}$

But also given that,

Area of the trapezium = 1080 cm²

${\sf{\implies\: 1080cm^2\: =\: {\dfrac{1}{2}}\: \times\: (50\: +\: 40)\: \times\: h}}$

${\sf{\implies\: 1080cm^2\: =\: {\dfrac{1}{2}}\: \times\: 90\: \times\: h}}$

${\sf{\implies\: 1080cm^2\: =\: 45h}}$

${\sf{\implies\: h\:=\: {\dfrac{1080}{45}}}}$

${\sf{\implies\: h\:=\: {\dfrac{120}{5}}}}$

${\sf{\implies\: h\:=\: 24}}$

Therefore, height of the trapezium is 24 cm