Quadrilaterals and Polygons: Trapezoids and Kites

Area of Trapezoids and Kites

Similar to the other figures we have studied; we can find the area of trapezoids and kites.

To find the area of a trapezoid, multiply one-half times the sum of the bases times the height.

 

Trapezoids:  one-half the quantity b sub 1 plus b sub 2, the quantity times h> , where b1 and b2 are the lengths of the bases and h is the height measured perpendicular to the parallel bases


To find the perimeter of an isosceles trapezoid, add base 1 plus base 2 plus two times leg 1.

Example:
The area of this trapezoid is 60 cm2.  Find the value of x.

trapezoid with one base measuring 3x minus 7 centimeters, the other base measuring 4x minus 1 centimeter, and the height measuring 6 centimeters

Solution
We can set up an equation with the formula for the area.

one-half the quantity b sub 1 plus b sub 2, the quantity times h; 60 equals one-half the quantity 3 x plus 7 plus 4x minus 1, the quantity times 6; 60 equals 3 the quantity 7 x minus 8; 60 equals 21 x minus 24; 84 equals 21 x; x equals 4

To find the area of a kite, multiply one-half times the product of the diagonals.

Kites: A = one-half the quantity d sub 1 plus d sub 2 , where d1 and d2 are the lengths of the diagonals


We will look at an example of finding the area of a kite on the next page.