570

Explanation

The trapezoid consists of two smaller shapes: a triangle and a rectangle. Draw a line from point A across this figure to form the two shapes. Find the area of each shape and then add them together to find the area of the trapezoid.

Area of rectangle = length x width.

Therefore, the area of the rectangle is 18x20 = 360

Area of a triangle = 1/2(base)(height).

The base of the triangle is 20.

The height of the triangle is unknown.

Use the Pythagorean Theorem to find the triangle's height. \(c^{2}=a^{2}+b^{2}\)where c is the triangle's hypotenuse.

\(29^{2}=20^{2}+(\text { height })^{2}\)

\(841=400+(\text { height })^{2}\)

\(441=(\text { height })^{2}\)

The square root of 441 is 21

height = 21.

Therefore, area of the triangle = (1/2)(20)(21) = 210. The total area of the trapezoid = 360+210 = 570.

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