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# How do you calculate the area of anisosceles trapezoid if you only know the width of the base and the length and angle of the sides?

One way would be as follows:

Let b represent the length of the base, l the length of each of the two sides, and theta the angle between the base and the two sides of length l. Now drop a perpendicular line from each vertex at the top of the trapezoid to the base. This yields two right triangles and a rectangle in the middle. The height of each right triangle (as well as the height of the rectangle) equals l*sin(theta) [because sin(theta)=opposite/hypotenuse] and the length of the base of each right triangle is l*cos(theta). The base of the rectangle is b minus the lengths of the two right triangles.

Area of the trapezoid=2*area of each right triangle+area of the rectangle=2*(1/2)*(l*sin(theta)*l*cos(theta))+(b-2*l*cos(theta))(l*sin(theta))=)*(l*sin(theta)*l*cos(theta))+(b-2*l*cos(theta))(l*sin(theta))=b*l*sin(theta)-l2*sin(theta)*cos(theta) Study guides

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## Properties that describe the appearance of matter are known as what properties

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