Lesson Worksheet: Finding the Area of a Triangle Using Trigonometry Mathematics • 11th Grade

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:

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

  • A12๐‘Ž๐‘๐ถsin
  • B14๐‘Ž๐‘๐ถcos
  • C13๐‘Ž๐‘๐ถsin
  • D14๐‘Ž๐‘๐ถsin
  • E12๐‘Ž๐‘๐ถcos

Q2:

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

Q3:

A small triangular flower bed has measurements as shown in the diagram. Calculate its area in square feet. Give your answer to two decimal places.

Q4:

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

  • A92โˆš3 cm2
  • B94 cm2
  • C94โˆš3 cm2
  • D18โˆš3 cm2
  • E9 cm2

Q5:

๐ด๐ต๐ถ is a triangle, where ๐ต๐ถ=15cm, ๐ด๐ถ=25cm, and ๐‘šโˆ ๐ถ=41โˆ˜. Find the area of ๐ด๐ต๐ถ, giving your answer to three decimal places.

Q6:

An isosceles triangle has two sides of length 48 cm and base angles of 73โˆ˜. Find the area of the triangle giving the answer to three decimal places.

Q7:

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

Q8:

๐ด๐ต๐ถ๐ท is a parallelogram, where ๐ด๐ต=41cm, ๐ต๐ถ=27cm, and ๐‘šโˆ ๐ต=159โˆ˜. Find the area of ๐ด๐ต๐ถ๐ท, giving the answer to the nearest square centimeter.

Q9:

๐ด๐ต๐ถ๐ท is a rhombus with a side length of 24 cm and an interior angle of 79โˆ˜. Find the area of the rhombus giving the answer to the nearest hundredth.

Q10:

๐ด๐ต๐ถ is a triangle where ๐ด๐ต=18cm, ๐‘šโˆ ๐ต=60โˆ˜ and the area of the triangle is 74โˆš3 cm2. Find length ๐ต๐ถ giving the answer to two decimal places.

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