CW-Area of Triangles Using Trig

Front

What is the formula for the area of a triangle using trigonometry?

Back

The area of a triangle can be calculated using the formula: \( A = \frac{1}{2}ab \sin(C) \), where \( a \) and \( b \) are the lengths of two sides and \( C \) is the included angle.

Front

Define the term 'included angle' in the context of triangles.

Back

The included angle is the angle formed between two sides of a triangle.

Front

How do you find the area of a triangle when you know two sides and the included angle?

Back

Use the formula: \( A = \frac{1}{2}ab \sin(C) \), where \( a \) and \( b \) are the lengths of the sides and \( C \) is the included angle.

Front

What is the area of a triangle with sides of length 7 cm and 10 cm, and an included angle of 30 degrees?

Back

Using the formula: \( A = \frac{1}{2} \times 7 \times 10 \times \sin(30^\circ) = 35 \text{ cm}^2 \).

Front

What is the relationship between the area of a triangle and its height?

Back

The area of a triangle can also be calculated using the formula: \( A = \frac{1}{2} \times base \times height \).

Front

Define a regular hexagon.

Back

A regular hexagon is a six-sided polygon where all sides and angles are equal.

Front

What is the formula for the area of a regular hexagon?

Back

The area of a regular hexagon can be calculated using the formula: \( A = \frac{3\sqrt{3}}{2} s^2 \), where \( s \) is the length of a side.

Front

How do you calculate the area of a triangle using Heron's formula?

Back

Heron's formula states that the area \( A \) of a triangle with sides of lengths \( a \), \( b \), and \( c \) is given by: \( A = \sqrt{s(s-a)(s-b)(s-c)} \), where \( s = \frac{a+b+c}{2} \) is the semi-perimeter.

Front

What is the semi-perimeter of a triangle?

Back

The semi-perimeter of a triangle is half the sum of the lengths of its sides, calculated as \( s = \frac{a+b+c}{2} \).

Front

If a triangle has an area of 50 cm² and a base of 10 cm, what is the height?

Back

Using the formula \( A = \frac{1}{2} \times base \times height \), we can rearrange to find height: \( height = \frac{2A}{base} = \frac{2 \times 50}{10} = 10 \text{ cm} \).