Area of Non-right Triangles Practice

1. Calculate the area of a triangle with sides measuring 8 cm, 10 cm, and 12 cm using Heron's formula.

Solution:
First, calculate the semiperimeter of the triangle:
s = (8 + 10 + 12) / 2
s = 30 / 2
s = 15 cm

Now, calculate the area using Heron's formula:
A = √[s(s - a)(s - b)(s - c)]
A = √[15(15 - 8)(15 - 10)(15 - 12)]
A = √[15(7)(5)(3)]
A = √(3150)
A ≈ 56.20 cm²

Therefore, the area of the triangle is approximately 56.20 cm².

2. Calculate the area of a triangle with a base of 6 cm and a height of 8 cm.

Solution:
Using the formula for the area of a triangle:
A = 1/2 * base * height
A = 1/2 * 6 cm * 8 cm
A = 24 cm²

Therefore, the area of the triangle is 24 cm².

3. Calculate the area of a triangle with sides measuring 5 cm, 7 cm, and 9 cm using Heron's formula.

Solution:
First, calculate the semiperimeter of the triangle:
s = (5 + 7 + 9) / 2
s = 21 / 2
s = 10.5 cm

Now, calculate the area using Heron's formula:
A = √[s(s - a)(s - b)(s - c)]
A = √[10.5(10.5 - 5)(10.5 - 7)(10.5 - 9)]
A = √[10.5(5.5)(3.5)(1.5)]
A = √(271.6875)
A ≈ 16.47 cm²

Therefore, the area of the triangle is approximately 16.47 cm².