Question 1136847
the longer base is equal to 8 cm.
the height is equal to 3 cm.
the slant height is equal to 5 cm.


if it is a right trapezoid, then two of the angles have to be right angles.


label your trapezoid ABCDE clockwise from top left.


angle A and angle E are right angles.


the slant height is side BC = 5.


the height is  BD = 3 and AE = 3.


the triangle on the right is right triangle BCD where the 90 degree angle is BDC.


angles BDE and ABD are also right angles.


use pythagorus to find the length of DC, which is 4.


pythagorus says 3^2 + x^2 = 5^2


solve for x to get x = sqrt(5^2 - 3^2) = sqrt(16) = 4.


that makes ED = 4 and, consequently AB = 4 because ABDE forms a rectangle.


the area of the trapezoid is equal to the area of the rectangle plus the area of the triangle.


this becomes 4 * 3 + 1/2 * 3 * 4 which becomes 12 + 6 = 18.


here's my diagram.


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