# 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.

**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 cm^{2}. 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 cm^{2}. 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 cm^{2}
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 cm
^{2} - B cm
^{2} - C cm
^{2} - D cm
^{2} - E9 cm
^{2}

**Q18: **

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

- A cm
^{2} - B cm
^{2} - C cm
^{2} - D cm
^{2}

**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.

**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.