Question

the perimeter of an isosceles trapezoid is 110 metre and the base are 40 metre and 30 metre in length calculate the length of the non parallel sides of the trip enjoyed and its area​

Answer 1

Answer:

Length of each non parallel sides : 20 m.

Area of the Trapezoid = 175√15 m²

                                     = 677.77 m²

Step-by-step explanation:

Given:

Perimeter of the isosceles trapezoid = 110 m.

Let, Length of the two parallel sides a = 40 m and b = 30 m.

Find the Length of the non parallel sides:

Let length of each non parallel sides of the isosceles trapezoid be y m.

[∵ In isosceles trapezium length of the two non parallel are equal.]

∴Perimeter of the trapezium = Sum of all the sides

⇒110 = (30 + 40 +2y)

⇒110 - 70 = 2y

⇒40 = 2y

⇒y = 20 m.

∴Length of each non parallel sides is 20 m.

Find the Area:

Let height (distance between two parallel sides) be h m.

∴By applying Pythagoras Theorem,

20² = 5² + h²

⇒400 - 25 = h²

⇒375 = h²

⇒√375 = h

⇒5√15 = h  

Area of the trapezium = $\frac{1}{2} * (Sum of the two parallel sides) * height$

                                   = 1/2 x(30+40) x 5√15 m²

                                   = 35 x 5√15 m²

                                   = 175√15 m²

∴Area of the trapezoid is 175√15 m²=  677.77 m²

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