Question

The perimeter of an isosceles trapezoid is 110m and the bases are 40m and 30m in length. calculate the length of the non- parallel sides of the tralezoid 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 = $\frac{1}{2} * (a+b) *height$

                                   = 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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