A wooden are is in the shape of a trapezium whose bases measure 128m and 92m and its height is 40m. A 4m wide walkway is constructed which runs perpendicular from the 2 bases. Calculate the area of the trapezium except the wooden walk way.
Answers
The area of the trapezium except for the wooden walkway which is 4m wide and is constructed running perpendicular from the 2 bases is 4240 m².
Step-by-step explanation:
Step 1:
The bases of the trapezium are 128 m & 92 m
The height of the trapezium = 40 m
The formula for the area of trapezium is given by,
Area = ½ x [sum of lengths of the parallel sides] x [perpendicular distance between parallel sides]
Therefore, based on the formula and substituting the values, we get
The area of the trapezium-shaped wooden arc (including the walkway)
= ½ * [128 + 92] * 40
= ½ * 220 * 40
= 110 * 40
= 4400 m²
Step 2:
It is given that a walkway of 4 m wide and perpendicular to the bases of the trapezium is constructed .
So, the area of the walkway = 4 * 40 = 160 m² ….. [Formula: area of rectangle = length * breadth]
Thus,
The area of the trapezium-shaped wooden arc except the walkway is given by,
= [Area of the trapezium-shaped wooden arc (including the walkway)] – [Area of the walkway]
= 4400 – 160
= 4240 m²
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