Area of Non-right Triangles practice
1) Find the area of a triangle with base 8 cm and height 6 cm.
Area = 1/2 * base * height
Area = 1/2 * 8 cm * 6 cm
Area = 24 square cm
2) Find the area of a triangle with sides measuring 5 cm, 7 cm, and 9 cm.
First, calculate the semi-perimeter:
s = (5 cm + 7 cm + 9 cm) / 2
s = 10.5 cm
Then, use Heron's formula to find the area:
Area = √[10.5 cm * (10.5 cm - 5 cm) * (10.5 cm - 7 cm) * (10.5 cm - 9 cm)]
Area = √[10.5 cm * 5.5 cm * 3.5 cm * 1.5 cm]
Area = √(326.25) square cm
Area ≈ 18.06 square cm
3) Find the area of a triangle with angles measuring 30 degrees, 60 degrees, and 90 degrees, and a side of length 10 cm.
First, find the height of the triangle using trigonometry:
sin(60 degrees) = height / 10 cm
height = 10 cm * sin(60 degrees)
height ≈ 8.66 cm
Then, use the formula for the area of a triangle:
Area = 1/2 * base * height
Area = 1/2 * 10 cm * 8.66 cm
Area ≈ 43.3 square cm
4) Find the area of a triangle with sides measuring 12 cm, 9 cm, and 15 cm.
First, calculate the semi-perimeter:
s = (12 cm + 9 cm + 15 cm) / 2
s = 18 cm
Then, use Heron's formula to find the area:
Area = √[18 cm * (18 cm - 12 cm) * (18 cm - 9 cm) * (18 cm - 15 cm)]
Area = √[18 cm * 6 cm * 9 cm * 3 cm]
Area = √(2916) square cm
Area ≈ 54 square cm