The bases of the trapezium are 18 and 24. the side equal to 14 forms an angle of 150 degrees with
| February 1, 2021 | education
The bases of the trapezium are 18 and 24. the side equal to 14 forms an angle of 150 degrees with one of the bases of the trapezoid, find the area of the trapezoid.
Let’s draw the ВН height from the top of an obtuse angle at 150
Consider a right-angled triangle ABН, and determine the magnitude of the acute angles. Angle ABН = 150 – 90 = 60, then angle ABН = 180 – 90 – 60 = 30.
The ВН leg lies opposite an angle of 30, and therefore is equal to half the length of the hypotenuse AB.
ВН = AB / 2 = 14/2 = 7 cm.
Determine the area of the trapezoid.
S = (AD + BC) * ВН / 2 = (24 + 18) * 7/2 = 147 cm2.
Answer: The area of the trapezoid is 147 cm2.
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