# Worksheet: Finding the Area of Triangle Using Trigonometry

In this worksheet, we will practice finding the area of a triangle without having to calculate its perpendicular height.

**Q7: **

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.

**Q8: **

An isosceles triangle has a side length of 48 cm and a base angle of . Find the area of the triangle giving the answer to three decimal places.

**Q9: **

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

**Q10: **

is a triangle, where
is obtuse, ,
, and the area is 106 cm^{2}. Find the length of , giving the answer to two decimal places.

**Q11: **

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

**Q12: **

is a triangle where ,
, the area is 167 cm^{2} and the radius of the circumcircle is 17 cm. Find length giving the answer to two decimal places.

**Q13: **

is a triangle, where ,
, and the area is
480 cm^{2}.
Find the length of giving the answer to the nearest centimeter.

**Q14: **

is an acute-angled triangle where , and the area is
315 cm^{2}. Find
, giving the answer to the nearest minute.

- A
- B
- C
- D

**Q15: **

is a triangle where , , and the radius of the circumcircle is 22.4 cm. Find the area of the triangle giving the answer to one decimal place.

**Q16: **

is a triangle where , and the perimeter is 59.34 cm. Find the area of the triangle giving the answer to two decimal places.

**Q17: **

is a triangle where ,
and the area is 197 cm^{2}. Find the perimeter of
and the circumference of the circumcircle giving
the answer to two decimal places.

- Aperimeter is 41.65 cm and circumference is 39.75 cm.
- Bperimeter is 41.65 cm and circumference is 79.5 cm.
- Cperimeter is 64.96 cm and circumference is 79.5 cm.
- Dperimeter is 64.96 cm and circumference is 39.75 cm.

**Q18: **

is a triangle where and . The point lies on where and bisects . Find the area of to two decimal places.

**Q19: **

The area of the triangle is and the radius of the circumcircle is . Find the value of .

- A
- B1
- C4
- D2

**Q20: **

is a triangle where , and the diameter of the circumcircle is 27 cm. Find the area of the triangle giving the answer to two decimal places.

**Q21: **

is a triangle where , and the area of
is 153 cm^{2}. Find
giving the answer to two decimal places.

**Q22: **

is an isosceles triangle where , and the perimeter is 31.31 cm. Find the area of the triangle giving the answer to two decimal places.

**Q24: **

is a triangle where ,
and the area of the triangle is cm^{2}. Find the length of
giving the answer to two decimal places.

**Q25: **

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