Worksheet: Heron’s Formula

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

Q1:

𝐴𝐡𝐢 is a triangle where 𝐴𝐡=50cm, 𝐡𝐢=30cm, and 𝐴𝐢=42cm. Find the area of the triangle giving the answer to the nearest square centimeter.

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 𝐴𝐢 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=(△𝐴𝐡𝐢)𝑃Area, where 𝑃 is half of the triangle’s perimeter.

  • A6√21 cm
  • B314√6 cm
  • C37√21 cm
  • D6√42 cm

Q8:

𝐴𝐡𝐢𝐷 is a quadrilateral, where π‘šβˆ π΅=90∘, 𝐴𝐡=8cm, 𝐡𝐢=6cm, 𝐴𝐷=39cm, and 𝐢𝐷=30cm. Find the area of 𝐴𝐡𝐢𝐷 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 106∘. 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 117∘. What is the area of this quadrilateral?

Q11:

𝐴𝐡𝐢 is a triangle, where 𝐡𝐢=28 cm, 𝐴𝐢=20 cm, and 𝐴𝐡=24 cm. Find the area of 𝐴𝐡𝐢 giving the answer to the nearest square centimeter.

Q12:

𝐴𝐡𝐢 is a triangle where 𝐴𝐡=27cm, 𝐡𝐢=24cm, and 𝐴𝐢=10cm. Find the area of the triangle giving the answer to the nearest square centimeter.

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