Areas of Parallelograms and Triangles Geometry Unit 4, Lesson 1

Theorem 5-2: Area of a Parallelogram The area of a parallelogram is the product of any base and the corresponding height A = bh Any side of the parallelogram can be called the base

Definitions Altitude – any segment perpendicular to the line containing the base drawn from the side opposite the base.

Definitions Height – the length of the altitude.

Find the Area Find the Area of the given Parallelogram: A = bh = (12in)(10in) = 120in 2 12in 10in 8in

Example 1 In parallelogram ABCD, DE and CF are altitudes. Find CF to the nearest tenth. HINT: Find the area of the parallelogram first then use the area formula to find CF.

Example 2 A parallelogram has sides 15 cm and 18cm. The altitude perpendicular to the containing 15 cm side is 9 cm long. Sketch the parallelogram. Then find the length of the altitude perpendicular to the line containing the 18 cm side.

Theorem 5-3: Area of a Triangle The area of a triangle is half the product of any base and the corresponding height. A = ½bh You can choose any side to be the base The corresponding height is the length of an altitude drawn to the line containing the base

Find the Area: Find the area of the given triangle Area = ½bh = ½(15cm)(8cm) = 60cm 2 15 cm 8 cm