Sine Formula and Area Calculations

The video tutorial covers methods to calculate the area of triangles using Heron's theorem and the sine formula. It explains Heron's theorem for side-side-side triangles and the sine formula for side-angle-side triangles. The tutorial also demonstrates applying these formulas to find the area of polygons like pentagons, parallelograms, and octagons, both inscribed and circumscribed in circles.

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

• Use the sine of the included angle.

• Find the semi-perimeter of the triangle.

• Calculate the height of the triangle.

• Determine the base of the triangle.

In the sine formula for finding the area of a triangle, what does the 'a' represent in 1/2 BC sin(a)?

• The included angle between sides B and C.

• The height of the triangle.

• The length of side a.

• The semi-perimeter of the triangle.

How is the height of a triangle determined when using the sine formula?

• By using the cosine of the angle.

• By multiplying the base by the sine of the angle.

• By adding the lengths of the sides.

• By dividing the base by the sine of the angle.

What is the area of a triangle with side lengths 9 and 5.2 and an included angle of 102 degrees using the sine formula?

• 18.5 square meters

• 22.9 square meters

• 25.4 square meters

• 30.1 square meters

When using the sine formula to find the area of a pentagon, what is the central angle if the pentagon is divided into five triangles?

• 108 degrees

• 60 degrees

• 72 degrees

• 90 degrees

How do you find the area of a parallelogram using Heron's theorem?

• By finding the area of one triangle and doubling it.

• By calculating the perimeter and dividing by two.

• By using the base times height formula.

• By using the sine of the included angle.

What is the central angle of an octagon when using the sine formula to find its area?

• 90 degrees

• 30 degrees

• 45 degrees

• 60 degrees

How is the area of an octagon inscribed in a circle calculated using the sine formula?

• By dividing the circle into four equal parts.

• By using the radius and the central angle.

• By calculating the perimeter of the octagon.

• By using the apothem and the side length.

What is the difference in area between an octagon inscribed in a circle and one circumscribed about a circle?

• The inscribed octagon has a larger area.

• The area cannot be determined.

• The circumscribed octagon has a larger area.

• Both have the same area.

What is the formula used to find the area of a regular polygon using the sine formula?

• Base times height

• 1/2 base times height

• 1/2 perimeter times apothem

• 1/2 BC sin(a)