Section 8.2: Areas of Triangles, Trapezoids, & Kites
The formula for calculating the area of triangles comes from dividing a parallelogram in half, so the area is half of base times height. When finding the area of a triangle, the height is an altitude and the base must be the side intersected by the altitude. When given the area and asked for a base or height, a common mistake is to forget to multiply both sides of the equation by 2 before dividing.
The area formula for a trapezoid is found by making a parallelogram made up of two congruent trapezoids. To do this, copy a trapezoid, rotate the copy 180 degrees, and translate to create a parallelogram. The area of a parallelogram is base times corresponding height; since there are two trapezoids, the area of trapezoids formula must be divided in half. Since the bases are not congruent, they must be summed separately.
The area formula for a kite is found by rearranging the pieces formed by the diagonals into a rectangle. Since one side is half of a diagonal, the area of a rhombus formula is one half the product of the diagonals. An additional formula for the area of a rhombus is to use the kite formula (it works because rhombuses are technically kites). Related topics includearea of parallelograms and solving formulas.
The area formula for a trapezoid is found by making a parallelogram made up of two congruent trapezoids. To do this, copy a trapezoid, rotate the copy 180 degrees, and translate to create a parallelogram. The area of a parallelogram is base times corresponding height; since there are two trapezoids, the area of trapezoids formula must be divided in half. Since the bases are not congruent, they must be summed separately.
The area formula for a kite is found by rearranging the pieces formed by the diagonals into a rectangle. Since one side is half of a diagonal, the area of a rhombus formula is one half the product of the diagonals. An additional formula for the area of a rhombus is to use the kite formula (it works because rhombuses are technically kites). Related topics includearea of parallelograms and solving formulas.
Notes and Powerpoints
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