A farm covers land in the shape of a trapezium. The length of the northern boundary of the farm is 265 m and length of the southern boundary

Question

A farm covers land in the shape of a trapezium. The length of the northern boundary of the farm is 265 m and length of the southern boundary is 180 m. The perpendicular distance from the northern end to the southern end is 90 m.
a Draw a diagram of the farm and find its area to the nearest square metre.
b Write your answer to part a to the nearest hectare.
c The farmer decides to purchase his neighbour’s farm, which is in the shape of a rectangle but has the same area as his farm. What are possible dimensions neighbour’s farm? Give your answer in metres.

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Thiên Thanh 2 weeks 2021-08-29T19:42:02+00:00 1 Answers 0 views 0

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    2021-08-29T19:43:27+00:00

    Answer:

    Step-by-step explanation:

    Part A

    Givens

    b1 = 265

    b2 = 180

    h  = 90

    Formula

    Area = (b1 + b2)*h / 2

    Solution

    Area = (265 + 180) * 90 / 2

    Area = 445 * 90 / 2

    Area = 40050 / 2

    Area = 20025 square meters

    Part B

    1 hectare = 10000 square meters

    x hectare = 20025 square meters         Cross multiply

    x * 10000 = 20025 * 1                             Divide by 10000

    x  = 20025 / 10000

    x = 2.0025

    Rounded to the nearest hectare that would be 2

    Part C

    The best shape is a square.

    That would mean that the area is given by

    s^2 = 20025

    sqrt(s^2) = sqrt(20025)

    s = 141.51

    Each side of the rectangle (square) = 141.51

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