The length of the fence of a trapezium-shaped field ABCD is 130 m and

1.	The length of the fence of a trapezium-shaped field ABCD is 130 m and side AB is perpendicular to each of the parallel sides AD and BC. If BC = 54m, CD = 19m and AD = 42m, find the area of the field.
Answer» Given Length of parallel sides AD = 42 m BC = 54 m Given that total length of fence is 130 m That is AB + BC +CD + DA = 130 AB + 54 + 19 + 42 = 130 Therefore AB = 15 Height (AB) = 15 m We know that area of trapezium is \(\frac{1}{2}\)× (sum of parallel sides) × height Therefore Area of trapezium = \(\frac{1}{2}\)× (42 + 54) × 15 = 720 m²

The length of the fence of a trapezium-shaped field ABCD is 130 m and side AB is perpendicular to each of the parallel sides AD and BC. If BC = 54m, CD = 19m and AD = 42m, find the area of the field.

Answer»

Given

Length of parallel sides

AD = 42 m

BC = 54 m

Given that total length of fence is 130 m

That is AB + BC +CD + DA = 130

AB + 54 + 19 + 42 = 130

Therefore AB = 15

Height (AB) = 15 m

We know that area of trapezium is \(\frac{1}{2}\)× (sum of parallel sides) × height

Therefore Area of trapezium = \(\frac{1}{2}\)× (42 + 54) × 15 = 720 m²