Calculating Triangle Area and Height

This video tutorial explains how to calculate the height of a triangle when the lengths of its three sides are known. It introduces Heron's formula to find the area of the triangle, which is then used to determine the height. The tutorial provides a step-by-step guide to calculating the semi-perimeter, using Heron's formula to find the area, and simplifying the expression for exact values. Finally, it demonstrates how to use the area to calculate the height, providing both exact and approximate decimal values.

What is the primary goal of the video tutorial?

• To explore different types of triangles and their properties.

• To understand how to find the height of a triangle using Heron's formula.

• To calculate the perimeter of a triangle using its sides.

• To learn how to calculate the area of a triangle using its base and height.

What is the formula for calculating the semi-perimeter (s) in Heron's formula?

• a * b * c

• (a * b * c) / 2

• (a + b + c) / 2

• a + b + c

Which of the following is NOT a step in calculating the area using Heron's formula?

• Calculate the semi-perimeter (s).

• Subtract each side from the semi-perimeter.

• Multiply the differences and take the square root.

• Divide the area by the base to find the height.

How is the area of the triangle expressed after simplification?

• 20 times the square root of 4

• 15 times the square root of 3

• 30 times the square root of 2

• 25 times the square root of 5

What is the approximate decimal value of the area of the triangle?

• 30.1234

• 42.4264

• 35.6789

• 50.5678

What is the formula used to calculate the height of the triangle from the area?

• Area = 2 * base * height

• Area = base / height

• Area = base * height

• Area = 0.5 * base * height

What is the exact value of the height of the triangle?

• 5 times the square root of 2

• 8 times the square root of 2

• 6 times the square root of 2

• 7 times the square root of 2

What is the approximate decimal value of the height of the triangle?

• 7.485

• 8.485

• 9.485

• 10.485

What is the base of the triangle used in the calculations?

• 12

• 11

• 10

• 9

What is the final step in calculating the height of the triangle?

• Multiply the area by the base.

• Add the base to the area.

• Subtract the base from the area.

• Divide the area by the base.