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## 10.4 Area of Triangles and Trapezoids

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**Vocabulary**Areas of Triangles and Trapezoids What You'll Learn You will learn to find the areas of triangles and trapezoids. Nothing new!**h**b Areas of Triangles and Trapezoids Look at the rectangle below. Its area is bh square units. congruent triangles The diagonal divides the rectangle into two _________________. 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.**Height**Base Areas of Triangles and Trapezoids Consider the area of this rectangle A(rectangle) = bh**h**b Areas of Triangles and Trapezoids a base of b units, and a corresponding altitude of h units, then**18 mi**6 yd 23 mi Areas of Triangles and Trapezoids Find the area of each triangle: A = 207 mi2 A = 13 yd2**height**base Because the opposite sides of a parallelogram have the same length,the area of a parallelogram is closely related to the area of a ________. Next we will look at the area of trapezoids. However, it is helpful to first understand parallelograms. rectangle height The area of a parallelogram is found by multiplying the ____ and the ______. base Base – the bottom of a geometric figure. Height – measured from top to bottom, perpendicular to the base.**b1**b2 h b2 b1 Areas of Triangles and Trapezoids Starting with a single trapezoid. The height is labeled h, and the bases are labeled b1 and b2 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 (b1 + b2) 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(b1 + b2) The area of the trapezoid is one-half of the parallelogram’s area.**b1**h b2 Areas of Triangles and Trapezoids bases of b1 and b2 units, and an altitude of h units, then**20 in**18 in 38 in Areas of Triangles and Trapezoids Find the area of the trapezoid: A = 522 in2**Areas of Triangles and Trapezoids**End of Lesson