Question

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

Answer 1

To find the area of the trapezium, we need to calculate the height and then use the formula for the area of a trapezium.

Step-by-step explanation:

Since side AB is perpendicular to both sides AD and BC, we can determine the height of the trapezium by using the Pythagorean theorem. The height (h) can be calculated as:

h = sqrt(AD^2 - (CD - BC)^2)

Substituting the given values, we have h = sqrt(42^2 - (19 - 54)^2) = sqrt(1764 - 1225) = sqrt(539) = 23.2 m.

The area (A) of the trapezium can be calculated using the formula:

A = ((AD + BC) / 2) * h

Substituting the given values, we have A = ((42 + 54) / 2) * 23.2 = 2469.6 square meters.

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