A parking lot has the shape of a parallelogram. The length of two adjacent sides are 70 meters and 100 meters. The angle between them is 70°. What is the area of the parking lot?
Answers
The area of the parking lot is 4606 square meter.
What is parallelogram?
It is a special type of quadrilateral that has both the pairs of opposite sides parallel and equal.
What is the area of parallelogram?
The area of a parallelogram is the product of its base and height.
We have,
length of two adjacent sides are 70meters and 100meters.
And base of parallelogram is 70m. (length of parallelogram is its base)
Angle between the adjacent sides is 70 degrees.
Let, side AB and BC be the two adjacent sides whose lengths are 70m and 100m.And h be the height of the parallelogram.
For the height of the parallelogram
In ΔADE, we have
[tex]sin70=\frac{DE}{AD}[/tex] [tex](sinx=\frac{perpendicular}{hypotenuse})[/tex]
⇒ [tex]0.9397=\frac{h}{70}[/tex]
⇒ [tex]0.9397[/tex]×70[tex]=h[/tex]
⇒ h=65.8m
Formula to find the area of parallelogram:
Area= base× height
so, the area of parking lot=base × height
substitute the value of base and height of the parallelogram in the above formula.
Therefore,
[tex]Area=65.8[/tex]×[tex]70[/tex]
[tex]Area=4606m^{2}[/tex]
Hence, the area of the parking lot is 4606 square meter.
Learn more about area of parallelogram here:
https://brainly.com/question/21576252
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