This document discusses three methods for calculating the area of triangles: using the base and height, using two sides and the included angle, and using all three sides. It provides the formulas for each method and works through examples of calculating the area. Practice problems are included at the end to allow additional practice applying the different area calculation methods.

1. Areas of Triangles
•Base and Height Given
•Two Sides and Included Angle Given
•Three Sides Given

2. Base and Height Given
h h
b b
A = ½bh

3. Find the area:
8
7
A = ½ bh

4. Find the area:
8
7
A = ½ bh
A = ½ (7)(8)
A = 28 units2

5. Two Sides and Included Angle
a
θ
b
ab
A = 2 sinθ

6. Find the area of the triangle below.

7. Find the area of the triangle below.
A = 5(8)/2 sin 35°
A = 11.5 m2

8. Three Sides Given
a c
(Heron’s Formula)
b
If the semiperimetersis:
Then Heron’s formula gives the area as:

9. Find the area:
Step 1: Find the semiperimeter
S = (7 + 8 + 10)/2

10. Find the area:
Step 1: Find the semiperimeter
S = (7 + 8 + 10)/2
S = 12.5

11. Find the area:
Step 2: Use Heron’s Formula

12. Find the area:
Step 2: Use Heron’s Formula
A = 27.8 in2

13. Additional Practice
Find the area of each:
1. 2.

14. Answers to practice problems.
1. 130 cm2 2. 45.1 in2