# 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:

Benjamin’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. Q6:

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. Q7:

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

• A
• B
• C
• D
• E

Q8:

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.

Q9:

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.

Q10:

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

Q11:

is a triangle, where is obtuse, , , and the area is 106 cm2. Find the length of , giving the answer to two decimal places.

Q12:

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

Q13:

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.

Q14:

is a triangle, where , , and the area is 480 cm2. Find the length of giving the answer to the nearest centimeter.

Q15:

is an acute-angled triangle where , and the area is 315 cm2. Find , giving the answer to the nearest minute.

• A
• B
• C
• D

Q16:

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.

Q17:

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

Q18:

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.

Q19:

is a triangle where and . The point lies on where and bisects . Find the area of giving the answer to the nearest whole number.

Q20:

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

• A
• B1
• C4
• D2

Q21:

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.

Q22:

is a triangle where , and the area of is 153 cm2. Find giving the answer to two decimal places.

Q23:

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:

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

Q25:

The Bermuda triangle is a region of the Atlantic Ocean whose boundary is made up of straight lines connecting Bermuda, Florida, and Puerto Rico. Given that Florida is 1,030 miles from Bermuda in the direction 24 degrees south of west and Puerto Rico is 980 miles from Bermuda in the direction 4 degrees west of south, find the area of the Bermuda triangle.