10.4 Area of Triangles and Trapezoids

You will learn to find the areas of triangles and trapezoids. Nothing new!

b h Look at the rectangle below. Its area is bh square units. The diagonal divides the rectangle into two _________________. congruent triangles The area of each triangle is half the area of the rectangle, or This result is true of all triangles and is formally stated in Theorem 10-3.

Consider the area of this rectangle A (rectangle) = bh Base Height

Theorem 10-3 Area of a Triangle If a triangle has an area of A square units, b h a base of b units, and a corresponding altitude of h units, then

Find the area of each triangle: A = 13 yd 2 6 yd 18 mi 23 mi A = 207 mi 2

Because the opposite sides of a parallelogram have the same length, the area of a parallelogram is closely related to the area of a ________. rectangle The area of a parallelogram is found by multiplying the ____ and the ______. base height base height Base – the bottom of a geometric figure. Height – measured from top to bottom, perpendicular to the base. Next we will look at the area of trapezoids. However, it is helpful to first understand parallelograms.

h b1b1 b2b2 b1b1 b2b2 Starting with a single trapezoid. The height is labeled h, and the bases are labeled b 1 and b 2 Construct a congruent trapezoid and arrange it so that a pair of congruent legs are adjacent. The new, composite figure is a parallelogram. It’s base is ( b 1 + b 2 ) and it’s height is the same as the original trapezoid. The area of the parallelogram is calculated by multiplying the base X height. A (parallelogram) = h(b 1 + b 2 ) The area of the trapezoid is one-half of the parallelogram’s area.

Theorem 10-4 Area of a Trapezoid If a trapezoid has an area of A square units, h b1b1 b2b2 bases of b 1 and b 2 units, and an altitude of h units, then

Find the area of the trapezoid: A = 522 in 2 18 in 20 in 38 in