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In this lesson, we will learn how to use Heron's formula to find the area of a triangle.

Q1:

π΄ π΅ πΆ is a triangle where π΄ π΅ = 5 0 c m , π΅ πΆ = 3 0 c m , and π΄ πΆ = 4 2 c m . Find the area of the triangle giving the answer to the nearest square centimetre.

Q2:

π΄ π΅ πΆ is a triangle where π΄ π΅ = 2 7 c m , π΅ πΆ = 2 4 c m , and π΄ πΆ = 1 0 c m . Find the area of the triangle giving the answer to the nearest square centimetre.

Q3:

Find the area of the quadrilateral giving the answer to three decimal places.

Q4:

Find the area of the figure below using Heronβs Formula, giving the answer to three decimal places.

Q5:

Q6:

π΄ π΅ πΆ π· is a quadrilateral, where π β π΅ = 9 0 β , π΄ π΅ = 8 c m , π΅ πΆ = 6 c m , π΄ π· = 3 9 c m , and πΆ π· = 3 0 c m . Find the area of π΄ π΅ πΆ π· giving the answer to the nearest hundredth.

Q7:

Find the area of the figure below using Heronβs Formula.

Q8:

The perimeter of the given rhombus is 292 cm and the length of π΄ πΆ is 116 cm. Use Heronβs Formula to calculate the area of the rhombus, giving the answer to three decimal places.

Q9:

In sequence, the four sides of a quadrilateral are of lengths 5.7, 7.2, 9.4, and 12.8. The angle between the two shortest sides is 1 0 6 β . What is the area of this quadrilateral?

Q10:

is a triangle, where cm, cm, and cm. Find the area of giving the answer to the nearest square centimetre.

Q11:

The lengths of a triangle are 12 cm, 5 cm, and 11 cm. Find the radius of the interior circle touching the sides using the formula π = ( β³ π΄ π΅ πΆ ) π A r e a , where π is half of the triangleβs perimeter.

Q12:

The four sequential sides of a quadrilateral have lengths 4.5 cm, 7.9 cm, 9.4 cm, and 12.9 cm. The angle between the two smallest sides is 1 1 7 β . What is the area of this quadrilateral?

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