Heron's Formula

Topics in this chapter

• Heron's Formula Fundamentals
• Special Triangles and Area
• Area Ratios and Scaling
• Triangle Heights and Medians
• Polygon and Quadrilateral Areas
• Heron's Formula Applications

Cheat sheet

Practice questions

1. Question 1Q-A04658

   What is the semi-perimeter $s$ of a triangle with side lengths $a$, $b$, and $c$?

   1. A.a + b + c
   2. B.(a + b + c) / 2
   3. C.(a + b + c) / 4
   4. D.2(a + b + c)
   See the answer and solution
2. Question 2Q-82F71A

   Heron's formula for the area of a triangle with sides $a$, $b$, $c$ and semi-perimeter $s$ is given by:

   1. A.\sqrt{s(s-a)(s-b)(s-c)}
   2. B.\sqrt{s(s+a)(s+b)(s+c)}
   3. C.s(s-a)(s-b)(s-c)
   4. D.\frac{1}{2} \sqrt{s(s-a)(s-b)(s-c)}
   See the answer and solution
3. Question 3Q-CCA229

   What is the area of an equilateral triangle whose side length is $4\text{ cm}$?

   1. A.4\sqrt{3}\text{ cm}^2
   2. B.8\sqrt{3}\text{ cm}^2
   3. C.16\sqrt{3}\text{ cm}^2
   4. D.2\sqrt{3}\text{ cm}^2
   See the answer and solution
4. Question 4Q-EEB208

   The sides of a triangular plot are in the ratio $3:5:7$ and its perimeter is $300\text{ m}$. What is its largest side?

   1. A.50 m
   2. B.100 m
   3. C.140 m
   4. D.150 m
   See the answer and solution
5. Question 5Q-526664

   Find the area of a triangle with side lengths $13\text{ cm}$, $14\text{ cm}$, and $15\text{ cm}$.

   1. A.84 cm^2
   2. B.90 cm^2
   3. C.65 cm^2
   4. D.42 cm^2
   See the answer and solution