# Lesson Worksheet: Finding the Area of a Triangle Using Trigonometry Mathematics

In this worksheet, we will practice finding the area of a triangle using the lengths of two sides and the sine of the included angle.

Q1:

is a triangle, where , , and . Find the area of , giving your answer to three decimal places.

Q2:

Find the area of the figure below giving the answer to three decimal places. Q3:

is a triangle where , , and . Find the area of the triangle giving the answer to two decimal places.

Q4:

In the given figure, work out the area of the triangle to 2 decimal places. Q5:

Which of the following is a formula that can be used to find the area of a triangle?

• A
• B
• C
• D
• E

Q6:

Find the area of a triangle whose two side lengths are 7 cm and 23 cm, and the angle included between them is .Give the answer to three decimal places.

Q7:

An isosceles triangle has two sides of length 48 cm and base angles of . Find the area of the triangle giving the answer to three decimal places.

Q8:

is an isosceles triangle where and is . Find the area of giving the answer correct to two decimal places.

Q9:

is a triangle where , and the area of the triangle is cm2. Find the length of giving the answer to two decimal places.

Q10:

In the triangle , , , and . Work out the area of the triangle to 2 decimal places.

Q11:

is a triangle where , , and the area of is 166 cm2. Find giving the answer to the nearest degree.

Q12:

is a triangle where , and . Find the area of the triangle giving the answer to one decimal place.

Q13:

The area of a quadrilateral is 533 cm2 where the lengths of the diagonals are 50 cm and 50 cm. Find the acute angle between the diagonals giving the answer to the nearest degree.

Q14:

A quadrilateral has diagonals which bisect each other. The diagonals have lengths of 18 cm and 9 cm and the included angle between them is . Find the area of the quadrilateral to the nearest square centimetre.

Q15:

is a rhombus with a side length of 24 cm and an interior angle of . Find the area of the rhombus giving the answer to the nearest hundredth.

Q16:

is a rhombus where the side length is 21 cm and . Find the area giving the answer to the nearest square centimeter.

Q17:

Find the area of an equilateral triangle with a side length of 3 cm, giving the answer in an exact form.

• A cm2
• B cm2
• C cm2
• D cm2
• E9 cm2

Q18:

Find the area of an equilateral triangle with side length cm.

• A cm2
• B cm2
• C cm2
• D cm2

Q19:

is a parallelogram, where , , and . Find the area of , giving the answer to the nearest square centimeter.

Q20:

In the given figure, has been extended to the point such that and are perpendicular. Work out the value of to 4 decimal places.

Work out the value of to 4 decimal places.

Work out the length of to 2 decimal places.

Work out the area of the triangle to 2 decimal places.

Q21:

In the given figure, , , and . Calculate the height to 2 decimal places.

Calculate the area of the triangle to 2 decimal places.

Q22:

In the given figure, , , and . Calculate the height to 2 decimal places.

Calculate the area of the triangle to 2 decimal places.

Q23:

Find the area of a triangular piece of land that measures 30 feet on one side and 42 feet on another, knowing that the included angle measures . Round your answer to the nearest whole square foot.

Q24:

Mason’s house is on a corner lot. Find the area of the front yard given that the edges measure 40 ft and 56 ft, as shown in the diagram. Q25:

A triangular piece of land measures 110 feet on one side and 250 feet on another, where the included angle measures . Find its area rounded to the nearest square foot.