# Worksheet: Heron's Formula

Q1:

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

• A 1β257 cm2
• B 528 cm2
• C 750 cm2
• D 629 cm2

Q2:

is a triangle where , , and . 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 Heronβs Formula, giving the answer to three decimal places.

Q5:

Find the area of the figure below using Heronβs Formula, giving the answer to three decimal places.

Q6:

is a quadrilateral, where , , , , and . Find the area of giving the answer to the nearest hundredth.

Q7:

Find the area of the figure below using Heronβs Formula.

Q8:

The perimeter of the given rhombus is 292 cm and the length of is 116 cm. Use Heronβ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 . 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 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 , where is half of the triangleβs perimeter.

• A cm
• B cm
• C cm
• D 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 . What is the area of this quadrilateral?