Triangle Area Calculation Methods

This video tutorial explains three methods to calculate the area of triangles. The first method uses the base and perpendicular height, suitable for right-angled triangles. The second method involves two known sides and an included angle, using the sine function. The third method applies Heron's formula for triangles with three known sides. Each method is demonstrated with examples, emphasizing the conditions under which each formula is applicable.

What is a common limitation of using the base and height method for calculating the area of a triangle?

• It is only applicable to isosceles triangles.

• It requires knowledge of all three angles.

• The base is not always perpendicular to the height.

• It can only be used for equilateral triangles.

Which formula is used when both the base and height of a triangle are known?

• 1/2 × base × height

• Cosine rule

• Sine rule

• Heron's formula

If a triangle has a base of 11 cm and a height of 10 cm, what is its area?

• 55 cm²

• 110 cm²

• 21 cm²

• 5.5 cm²

In the first condition, what is the angle between the base and height?

• 45 degrees

• 60 degrees

• 90 degrees

• 180 degrees

What is the area of a triangle with a base of 8 cm and a height of 3 cm?

• 12 cm²

• 24 cm²

• 8 cm²

• 16 cm²

Which condition requires the use of the sine function to calculate the area of a triangle?

• When the base and height are known

• When two sides and an angle are known

• When all three sides are known

• When the triangle is equilateral

What is the formula for calculating the area of a triangle when two sides and the included angle are known?

• a² + b² = c²

• 1/2 × a × b × sin(C)

• 1/2 × base × height

• Heron's formula

If a triangle has sides of 5 cm and 7 cm with an included angle of 30 degrees, what is the area?

• 8.75 cm²

• 17.5 cm²

• 15 cm²

• 10.5 cm²

Which formula is used when all three sides of a triangle are known?

• Sine rule

• 1/2 × base × height

• Cosine rule

• Heron's formula

What is the first step in applying Heron's formula?

• Find the sine of the angle

• Multiply the base and height

• Use the Pythagorean theorem

• Calculate the semi-perimeter