Area of Non-right Triangles Practice answers.

Answer 1

1. Find the area of a triangle with side lengths of 4, 7, and 8.
Using Heron's formula: s = (4 + 7 + 8) / 2 = 9.5
Area = √(9.5(9.5-4)(9.5-7)(9.5-8)) ≈ √(9.5*5.5*2.5*1.5) ≈ √(578.125) ≈ 24.05

2. Find the area of a triangle with side lengths of 5, 12, and 13.
Using Heron's formula: s = (5 + 12 + 13) / 2 = 15
Area = √(15(15-5)(15-12)(15-13)) = √(15*10*3*2) = √900 = 30

3. Find the area of a triangle with side lengths of 8, 15, and 17.
Using Heron's formula: s = (8 + 15 + 17) / 2 = 20
Area = √(20(20-8)(20-15)(20-17)) = √(20*12*5*3) = √1200 = 34.64

4. Find the area of a triangle with side lengths of 6, 8, and 10.
Since this is a right triangle, we can use the formula for the area of a triangle: 1/2 * base * height
Area = 1/2 * 6 * 8 = 24

5. Find the area of a triangle with side lengths of 9, 10, and 12.
Using Heron's formula: s = (9 + 10 + 12) / 2 = 15.5
Area = √(15.5(15.5-9)(15.5-10)(15.5-12)) = √(15.5*6.5*5.5*3.5) = √(2273.625) ≈ 47.70