Question
What is the volume of a triangle that has one side of 8 cm one side of 10 cm and one side of 4 cm?
150 cm, 152 cm, 160 cm or 172 cm
150 cm, 152 cm, 160 cm or 172 cm
Answers
GPT 3.5
To calculate the volume of a triangle, you will need the area of the triangle and the height from the base to the apex.
First, calculate the area of the triangle using Heron's formula:
s = (8 + 10 + 4) / 2 = 11 cm (semi-perimeter)
Area = √(s(s-8)(s-10)(s-4))
Area = √(11(11-8)(11-10)(11-4))
Area = √(11*3*1*7)
Area = √(231)
Area ≈ 15.20 cm^2
Now, calculate the height of the triangle using the area:
15.20 = (1/2) * 8 * h
15.20 = 4h
h = 3.80 cm
Finally, calculate the volume of the triangle:
Volume = (1/3) * area * height
Volume = (1/3) * 15.20 * 3.80
Volume = 15.20 * 1.267
Volume ≈ 19.27 cm
Therefore, the closest answer is 172 cm.
First, calculate the area of the triangle using Heron's formula:
s = (8 + 10 + 4) / 2 = 11 cm (semi-perimeter)
Area = √(s(s-8)(s-10)(s-4))
Area = √(11(11-8)(11-10)(11-4))
Area = √(11*3*1*7)
Area = √(231)
Area ≈ 15.20 cm^2
Now, calculate the height of the triangle using the area:
15.20 = (1/2) * 8 * h
15.20 = 4h
h = 3.80 cm
Finally, calculate the volume of the triangle:
Volume = (1/3) * area * height
Volume = (1/3) * 15.20 * 3.80
Volume = 15.20 * 1.267
Volume ≈ 19.27 cm
Therefore, the closest answer is 172 cm.