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:

𝐴𝐡𝐢 is a triangle, where 𝐡𝐢=15cm, 𝐴𝐢=25cm, and π‘šβˆ πΆ=41∘. Find the area of 𝐴𝐡𝐢, giving your answer to three decimal places.

Q2:

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

Q3:

𝐴𝐡𝐢 is a triangle where 𝐴𝐡=5cm, 𝐴𝐢=11cm, and π‘šβˆ π΄=107∘. 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?

  • A12π‘Žπ‘πΆsin
  • B14π‘Žπ‘πΆcos
  • C13π‘Žπ‘πΆsin
  • D14π‘Žπ‘πΆsin
  • E12π‘Žπ‘πΆcos

Q6:

Find the area of a triangle whose two side lengths are 7 cm and 23 cm, and the angle included between them is 101∘.Give the answer to three decimal places.

Q7:

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.

Q8:

𝐴𝐡𝐢 is an isosceles triangle where 𝐴𝐡=𝐴𝐢=11cm and π‘šβˆ π΄ is 158∘. Find the area of 𝐴𝐡𝐢 giving the answer correct to two decimal places.

Q9:

𝐴𝐡𝐢 is a triangle where 𝐴𝐡=18cm, π‘šβˆ π΅=60∘ and the area of the triangle is 74√3 cm2. Find the length of 𝐡𝐢 giving the answer to two decimal places.

Q10:

In the triangle 𝐴𝐡𝐢, 𝐴𝐢=8, 𝐡𝐢=5, and π‘šβˆ π΅πΆπ΄=44∘. Work out the area of the triangle to 2 decimal places.

Q11:

𝐴𝐡𝐢 is a triangle where 𝐴𝐡=30cm, 𝐡𝐢=39cm, and the area of 𝐴𝐡𝐢 is 166 cm2. Find π‘šβˆ π΅ giving the answer to the nearest degree.

Q12:

𝐴𝐡𝐢 is a triangle where π‘Ž=7.03cm, 𝑏=4.03cm and π‘šβˆ πΆ=75∘. 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 52∘. Find the area of the quadrilateral to the nearest square centimetre.

Q15:

𝐴𝐡𝐢𝐷 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.

Q16:

𝐴𝐡𝐢𝐷 is a rhombus where the side length is 21 cm and π‘šβˆ π΄π΅πΆ=64∘. 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.

  • A92√3 cm2
  • B94 cm2
  • C94√3 cm2
  • D18√3 cm2
  • E9 cm2

Q18:

Find the area of an equilateral triangle with side length π‘₯ cm.

  • A12π‘₯ cm2
  • Bπ‘₯ cm2
  • C√32π‘₯ cm2
  • D√34π‘₯ cm2

Q19:

𝐴𝐡𝐢𝐷 is a parallelogram, where 𝐴𝐡=41cm, 𝐡𝐢=27cm, and π‘šβˆ π΅=159∘. Find the area of 𝐴𝐡𝐢𝐷, giving the answer to the nearest square centimeter.

Q20:

In the given figure, 𝐡𝐴 has been extended to the point 𝐷 such that 𝐡𝐷 and 𝐷𝐢 are perpendicular.

Work out the value of sin110 to 4 decimal places.

Work out the value of sin70 to 4 decimal places.

Work out the length of 𝐷𝐢 to 2 decimal places.

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

Q21:

In the given figure, 𝐴𝐢=5, 𝐡𝐢=7, and π‘šβˆ π΅πΆπ΄=41∘.

Calculate the height 𝐴𝐷 to 2 decimal places.

Calculate the area of the triangle 𝐴𝐡𝐢 to 2 decimal places.

Q22:

In the given figure, 𝐴𝐡=6, 𝐡𝐢=11, and π‘šβˆ π΄π΅πΆ=61∘.

Calculate the height 𝐴𝐷 to 2 decimal places.

Calculate the area of the triangle 𝐴𝐡𝐢 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 132∘. 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 85∘. Find its area rounded to the nearest square foot.

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