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?

  • A12𝑎𝑏𝐶sin
  • B14𝑎𝑏𝐶cos
  • C13𝑎𝑏𝐶sin
  • D14𝑎𝑏𝐶sin
  • E12𝑎𝑏𝐶cos

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.

  • A923 cm2
  • B94 cm2
  • C943 cm2
  • D183 cm2
  • E9 cm2

Q5:

𝐴𝐵𝐶 is a triangle, where 𝐵𝐶=15cm, 𝐴𝐶=25cm, and 𝑚𝐶=41. Find the area of 𝐴𝐵𝐶, giving your answer to three decimal places.

Q6:

An isosceles triangle has two sides of length 48 cm and base angles of 73. 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:

𝐴𝐵𝐶𝐷 is a parallelogram, where 𝐴𝐵=41cm, 𝐵𝐶=27cm, and 𝑚𝐵=159. Find the area of 𝐴𝐵𝐶𝐷, giving the answer to the nearest square centimeter.

Q9:

𝐴𝐵𝐶𝐷 is a rhombus with a side length of 24 cm and an interior angle of 79. Find the area of the rhombus giving the answer to the nearest hundredth.

Q10:

𝐴𝐵𝐶 is a triangle where 𝐴𝐵=18cm, 𝑚𝐵=60 and the area of the triangle is 743 cm2. Find length 𝐵𝐶 giving the answer to two decimal places.

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