1. Given the parallelogram at right, we are able to determine that its area is equal to Activity You can use a parallelogram to find the area of a triangle. 1 12 5 2 3 4 Now watch as we draw a diagonal through the parallelogram. This forms two congruent triangles. How is the area of one triangle related to the area of the parallelogram? Use the rule for the area of a parallelogram to write a rule for the area of a triangle. Area of a Triangle 10 2. 5  12 = 60.

2. The base of a triangle is the length of any of its sides. The height of a triangle is the perpendicular distance between the side whose length is the base and the vertex opposite that side. NOTE BOOK Words Algebra Area of a Triangle A = bh 1212 Area of a triangle = base height 1212 h b Area of a Triangle 10 2.

3. Finding the Area of a Triangle EXAMPLE 1 Find the area of the triangle shown. 11 ft 4 ft A = bh 1212 Write the formula for the area of a triangle. Substitute 4 for b and 11 for h. Simplify. = bh 1212 = 22 ANSWER The area of the triangle is 22 square feet. Area of a Triangle 10 2. 4 11

4. Finding the Area of Combined Figures EXAMPLE 2 Tall Ships A pattern of a sail for a tall ship is shown. How much material, in square feet, is needed to make the sail? Find the area of each shape. A = 6 ANSWER You will need 30 square feet of material to make the sail. 4 ft 6 ft 3 ft SOLUTION 1 2 Area of the triangle:Area of the rectangle: A = 4 3 1212 A = 4 6 A = 24 Add the areas together to find the total area. 6 + 24 = 30 Area of a Triangle 10 2.

5. A = b h 1212 Finding the Height of a Triangle EXAMPLE 3 The area of a triangle is 36 square inches and the base is 8 inches. What is the height of the triangle? A = bh 1212 Write the formula for the area of a triangle. 36 = 4 h Substitute 36 for A and 8 for b. h = 36  4 Simplify. Write a related division equation. h = 9 Simplify. ANSWER The height of the triangle is 9 inches. Area of a Triangle 10 2. 368