Worksheet: Heron's Formula

In this worksheet, we will practice using Heron's formula to find the area of a triangle.

Q1:

𝐴 𝐡 𝐢 is a triangle where 𝐴 𝐡 = 5 0 c m , 𝐡 𝐢 = 3 0 c m , and 𝐴 𝐢 = 4 2 c m . Find the area of the triangle giving the answer to the nearest square centimetre.

Q2:

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

Q3:

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

Q4:

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

Q5:

Find the area of the figure below using Heron’s Formula.

Q6:

The perimeter of the given rhombus is 292 cm and the length of 𝐴 𝐢 is 116 cm. Use Heron’s Formula to calculate the area of the rhombus, giving the answer to three decimal places.

Q7:

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‘Ÿ = ( β–³ 𝐴 𝐡 𝐢 ) 𝑃 A r e a , where 𝑃 is half of the triangle’s perimeter.

  • A 6 √ 4 2 cm
  • B 6 √ 2 1 cm
  • C 3 1 4 √ 6 cm
  • D 3 7 √ 2 1 cm

Q8:

𝐴 𝐡 𝐢 𝐷 is a quadrilateral, where π‘š ∠ 𝐡 = 9 0 ∘ , 𝐴 𝐡 = 8 c m , 𝐡 𝐢 = 6 c m , 𝐴 𝐷 = 3 9 c m , and 𝐢 𝐷 = 3 0 c m . Find the area of 𝐴 𝐡 𝐢 𝐷 giving the answer to the nearest hundredth.

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 ∘ . What is the area of this quadrilateral?

Q10:

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 ∘ . What is the area of this quadrilateral?

Q11:

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

Q12:

𝐴 𝐡 𝐢 is a triangle where 𝐴 𝐡 = 2 7 c m , 𝐡 𝐢 = 2 4 c m , and 𝐴 𝐢 = 1 0 c m . Find the area of the triangle giving the answer to the nearest square centimetre.

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