# 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.

Q1:

is a triangle, where , , and . Find the area of , giving your answer to three decimal places.

Q2:

Find the area of the figure below giving the answer to three decimal places. Q3:

is a triangle where , , and . 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:

The figure shows a triangular field with sides 670 m, 510 m, and 330 m. Find the area of the field giving the answer to the nearest square meter. Q6:

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

• A
• B
• C
• D
• E

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 cm2. 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 cm2 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 cm2. Find the length of giving the answer to the nearest centimeter.

Q14:

is an acute-angled triangle where , and the area is 315 cm2. 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 cm2. 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 cm2. 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.

Q23:

Consider the following figure. Find an expression for the height in terms of , , and .

• A
• B
• C
• D
• E

Find an expression for the area of the triangle in terms of , , and .

• A
• B
• C
• D
• E

Q24:

is a triangle where , and the area of the triangle is cm2. 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.