Calculating Triangle Area with Heron's Formula

This video tutorial explores various methods to calculate the area of triangles, including right, isosceles, equilateral, and triangles with given sides and angles. It covers the basic formula of half base times height, the Pythagorean theorem for isosceles triangles, and Heron's formula for triangles with three sides. The tutorial also explains using trigonometry for triangles with two sides and an included angle.

What is the area of a right triangle with a base of 10 units and a height of 12 units?

• 24 square units

• 120 square units

• 30 square units

• 60 square units

What is the area of a triangle using the base and height method if the base is 8 units and the height is 6 units?

• 48 square units

• 24 square units

• 12 square units

• 18 square units

How do you find the height of an isosceles triangle with a base of 8 units and sides of 5 units each?

• Using the Pythagorean theorem

• Multiplying the base by two

• Adding the side lengths

• Dividing the base by two

How is the height of an isosceles triangle determined when the base and one side are known?

• By multiplying the base by the side

• By adding the base to the side

• By dividing the base by two and applying the Pythagorean theorem

• By subtracting the base from the side

What is the area of an equilateral triangle with each side measuring 10 units?

• 50 square units

• 25√3 square units

• 100 square units

• 75√3 square units

What formula is used to calculate the area of an equilateral triangle using only its side length?

• √3/4 * side^2

• √2/4 * side^2

• side^2/2

• side^3/4

Using the SAS condition, what is the area of a triangle with sides 15 and 10 units and an included angle of 30 degrees?

• 37.5 square units

• 7.5 square units

• 75 square units

• 150 square units

What is the area of a triangle using the SAS formula with sides 10 units and 15 units and an angle of 30 degrees between them?

• 37.5 square units

• 7.5 square units

• 75 square units

• 150 square units

What is the first step in applying Heron's formula to find the area of a triangle?

• Subtract each side from the semi-perimeter

• Find the semi-perimeter of the triangle

• Calculate the square root of the semi-perimeter

• Multiply all side lengths

What is the result of applying Heron's formula to a triangle with sides 9, 10, and 11 units?

• 15√2 square units

• 60 square units

• 45 square units

• 30√2 square units