Can anyone help me figure out this problem

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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

i you goofed up when writing this, because hnot is not a word minusf is not either. i cannot answer   because of that.

step-by-step explanation:

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