# Worksheet: Finding the Area of Triangle Using Trigonometry

Q1:

Benjaminβ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.

Q2:

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

Q3:

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

Q4:

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

Q5:

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

Q6:

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

Q7:

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

Q10:

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

• A
• B
• C
• D
• E

Q11:

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

Q12:

In the given figure, work out the area of the triangle to 2 decimal places.

Q13:

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.

Q14:

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.

Q15:

An isosceles triangle has a side length of 49 cm and a base angle of . Find the area of the triangle giving the answer to three decimal places.

Q16:

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

• A 43 cm
• B 39 cm
• C 12.5 cm
• D 25 cm

Q17:

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

• A
• B
• C
• D

Q18:

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.

Q19:

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

Q20:

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.

• A perimeter is 64.96 cm and circumference is 39.75 cm.
• B perimeter is 41.65 cm and circumference is 79.5 cm.
• C perimeter is 41.65 cm and circumference is 39.75 cm.
• D perimeter is 64.96 cm and circumference is 79.5 cm.

Q21:

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

Q22:

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

• A2
• B4
• C
• D1

Q23:

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.

Q24:

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

Q25:

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.