Can anyone help me figure out this problem
1 answer:
<h3>Answer: 192 square units</h3>
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Explanation:
Refer to the diagram below.
Draw a line through point D such that it is perpendicular to side BC. This new line intersects BC at point E.
In other words, E is on BC such that segments DE and BC are perpendicular.
Notice how triangle CED is a right triangle with legs DE and EC. The hypotenuse is DC = 16.
Let h be the height of the trapezoid. It's also the height of triangle CED where EC is the base. In other words, h = length of DE.
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Focus on triangle CED. We'll use the sine ratio to find h
sin(angle) = opposite/hypotenuse
sin(C) = DE/DC
sin(30) = h/16
0.5 = h/16
0.5*16 = h
8 = h
h = 8
The height of triangle CED is 8, so the height of the trapezoid is also 8.
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Apply the area of a trapezoid formula
Area = height*(base1+base2)/2
A = h*(b1+b2)/2
A = 8*(27+21)/2
A = 8(48)/2
A = 8*24
A = 192
The trapezoid's area is 192 square units
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