Identify the area of the trapezoid.
1 answer:
Option B: The area of the trapezoid is 157.5 m²
Explanation:
We need to determine the area of the trapezoid.
The area of the trapezoid can be determined by the formula,
where h is the height, a and b are the base of the trapezoid.
From the figure, it is obvious that ,
and
Substituting these values in the formula, we have,
Simplifying the terms, we have,
Multiplying the terms in the numerator, we have,
Dividing, we get,
Thus, the area of the trapezoid is 157.5 m²
Hence, Option B is the correct answer.
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First, you plot the coordinates to visualize the problem clearly. As you can see in the picture, the longest sides could either be one of those marked in red. This could be initially determined when you use visual estimation. We measure this using the distance formula: d = √[(x2-x1)^2 + (y2-y1)^2)]
Between coordinates (0,3) and (3,6)
d = √[(3-0)^2 + (6-3)^2)]
d= 4.24 units
Between coordinates (2,1) and (5,4)
d = √[(5-2)^2 + (4-1)^2)]
d= 4.24 units
They are of equal length. Both are the longest sides which measures 4.24 units.
Between coordinates (0,3) and (3,6)
d = √[(3-0)^2 + (6-3)^2)]
d= 4.24 units
Between coordinates (2,1) and (5,4)
d = √[(5-2)^2 + (4-1)^2)]
d= 4.24 units
They are of equal length. Both are the longest sides which measures 4.24 units.