Question

In a trapezium, the parallel sides measure 40 cm and 20 cm. Calculate the area of the trapezium if its non-parallel sides are equal having the lengths of 26 cm.

Answer 1

Answer:

The parallel sides of an isosceles trapezium = 40 cm and 20 cm.

The equal sides = 26 cm.

The distance between the parallel sides = [26^2-{(40–20)/2}^2]^0.5

= [676–10^2]^0.5

= (676–100)^0.5

= 576^0.5

= 24 cm.

Area of trapezium = (40+20)*24/2 = 720 sq cm. Answer.

Answer 2

Given,

Length of parallel sides = 40 cm , 20 cm

Length of non parallel sides = 26 cm

To find,

Area of the trapezium

Solution,

We may utilize the following mathematical approach.

The approach for obtaining the area of the trapezium is as follows.

We know that,

Length of parallel sides = 40 cm (a) and 20 cm (b)

Length of non parallel sides = 26 cm (c)

Now,

Height of the trapezium (h) = √ (c² - ($\frac{a-b}{2}$)²)

                                             = √ (26² - ($\frac{40-20}{2}$)²)

                                             = √ 26² - 10²

                                             =  √576

                                             = 24 cm

We know that,

Area of the trapezium = $\frac{1}{2}(a+b)*h$

                                     = $\frac{1}{2} (40+20)*24$

                                     = 60 * 12

                                     = 720 cm²

As a consequence, we may estimate the trapezium's area to be 720 cm².