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In this lesson, we will learn how to find the area of a triangle without having to calculate its perpendicular height.

Q1:

π΄ π΅ πΆ is a triangle, where π΅ πΆ = 1 5 c m , π΄ πΆ = 2 5 c m , and π β πΆ = 4 1 β . Find the area of π΄ π΅ πΆ , giving your answer to three decimal places.

Q2:

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

Q3:

π΄ π΅ πΆ is a triangle where π΄ π΅ = 5 c m , π΄ πΆ = 1 1 c m , and π β π΄ = 1 0 7 β . 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:

Magedβs 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 metre.

Q7:

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

Q8:

Find the area of a triangle whose two side lengths are 7 cm and 23 cm, and the angle included between them is 1 0 1 β .Give the answer to three decimal places.

Q9:

An isosceles triangle has a side length of 49 cm and a base angle of 4 4 β . Find the area of the triangle giving the answer to three decimal places.

Q10:

π΄ π΅ πΆ is an isosceles triangle where π΄ π΅ = π΄ πΆ = 1 1 c m and π β π΄ is 1 5 8 β . Find the area of π΄ π΅ πΆ giving the answer correct to two decimal places.

Q11:

π΄ π΅ πΆ is a triangle, where β π΄ πΆ π΅ is obtuse, π = 2 0 c m , π = 1 4 c m , and the area is 106 cm^{2}. Find the length of π΄ π΅ , giving the answer to two decimal places.

Q12:

π΄ π΅ πΆ π· is a parallelogram where π΄ π΅ = 9 . 3 c m , π β πΆ π΄ π΅ = 2 6 4 8 β² β and π β π· π΅ π΄ = 6 6 3 0 β² β . Find the area giving the answer to two decimal places.

Q13:

π΄ π΅ πΆ is a triangle where π = 2 3 c m , π = 2 1 c m , the area is 167 cm^{2} and the radius of the circumcircle is 17 cm. Find length π giving the answer to two decimal places.

Q14:

π π π is a triangle where π β π = 3 5 β , π β π = 6 2 β and the area is 480 cm^{2}. Find the length of π π giving the answer to the nearest centimetre.

Q15:

π΄ π΅ πΆ is an acute-angled triangle where π΄ πΆ = 3 0 c m , s i n π΄ = 0 . 7 and the area is 315 cm^{2}. Find π β π΅ , giving the answer to the nearest minute.

Q16:

π΄ π΅ πΆ is a triangle where π = 2 4 . 9 c m , π = 2 7 . 9 c m , π = 2 2 . 5 c m and the radius of the circumcircle is 22.4 cm. Find the area of the triangle giving the answer to one decimal place.

Q17:

π΄ π΅ πΆ is a triangle where π β π΄ = 6 4 β , π β πΆ = 7 1 β and the perimeter is 59.34 cm. Find the area of the triangle giving the answer to two decimal places.

Q18:

π΄ π΅ πΆ is a triangle where π β π΄ = 4 7 β , π β π΅ = 6 6 β and the area is 197 cm^{2}. Find the perimeter of π΄ π΅ πΆ and the circumference of the circumcircle giving the answer to two decimal places.

Q19:

Given that π΄ π΅ πΆ is a triangle where π β π΅ = 6 8 β and π β πΆ = 4 0 β . The point π· lies on π΅ πΆ where π΄ π· = 2 6 c m and bisects β π΄ . Find the area of β³ π΄ π΅ πΆ giving the answer to two decimal places.

Q20:

The area of the triangle π΄ π΅ πΆ is π₯ and the radius of the circumcircle is π . Find the value of 4 π π₯ π π π .

Q21:

π΄ π΅ πΆ is a triangle where π β π΅ = 6 6 β , π β πΆ = 6 3 β and the diameter of the circumcircle is 27 cm. Find the area of the triangle π΄ π΅ πΆ giving the answer to two decimal places.

Q22:

π΄ π΅ πΆ is a triangle where π β π΅ = 3 6 β , π β πΆ = 6 0 β and the area of π΄ π΅ πΆ is 153 cm^{2}. Find π giving the answer to two decimal places.

Q23:

π΄ π΅ πΆ is an isosceles triangle where π = π , π β π΄ = 4 2 β and the perimeter is 31.31 cm. Find the area of the triangle giving the answer to two decimal places.

Q24:

In the given figure.

Find an expression for the height β in terms of π , π , and πΆ .

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

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 0 3 0 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.

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