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Worksheet: Heron's Formula

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 centimeter.

  • A 1 257 cm2
  • B 528 cm2
  • C 750 cm2
  • D 629 cm2

Q2:

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 centimeter.

  • A 239 cm2
  • B 44 cm2
  • C 324 cm2
  • D 119 cm2

Q3:

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

Q6:

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.

Q7:

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

Q8:

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.

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:

𝐴 𝐡 𝐢 is a triangle, where 𝐡 𝐢 = 2 8 cm, 𝐴 𝐢 = 2 0 cm, and 𝐴 𝐡 = 2 4 cm. Find the area of 𝐴 𝐡 𝐢 giving the answer to the nearest square centimeter.

  • A 48 cm2
  • B 470 cm2
  • C 168 cm2
  • D 235 cm2
  • E 202 cm2

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‘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

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 ∘ . What is the area of this quadrilateral?