Exploring the Area of Triangles in Pre Calculus

What is the basic formula for the area of a triangle?

• Area = base + height

• Area = 1/2 * base * height

• Area = base * height

• Area = (base + height) / 2

How can the height of a triangle be calculated using trigonometry?

• Height = base * tan(angle)

• Height = base * cos(angle)

• Height = base * sin(angle)

• Height = base / sin(angle)

In the context of triangle area calculation, what does 'c' typically represent?

• The height of the triangle

• The longest side of the triangle

• The base of the triangle

• An angle of the triangle

What new formula was introduced for calculating the area of a triangle?

• Area = 1/2 * a * b * cos(c)

• Area = a * b * sin(c)

• Area = a * b * cos(c)

• Area = 1/2 * a * b * sin(c)

What is required to use the formula Area = 1/2 * a * b * sin(c)?

• Two angles and any side of the triangle

• The base and height of the triangle

• Three sides of the triangle

• Two sides and the angle between them

Under what condition is Heron's formula best used?

• When two sides and the included angle are known

• When two angles and a side are known

• When all three side lengths are known

• When the base and height are known

How do you calculate the semi-perimeter of a triangle?

• Divide the perimeter by 3

• Add the two shortest sides and divide by 2

• Multiply the longest side by 2

• Add all three sides and divide by 2

What is the area of a triangle with sides 15, 18, and angle C = 100 degrees?

• 132.949 square units

• 150 square units

• 120 square units

• 100 square units

For a triangle with sides 20, 40, and 30, what formula is used to find the area?

• Basic area formula

• Pythagorean theorem

• Trigonometric area calculation

• Heron's formula

What is the area of a parallelogram with sides 8 and 12, and one angle of 60 degrees?

• 96 radical three square units

• 48 radical three square units

• 48 square units

• 96 square units