Area of a Triangle Using Heron’s Formula

Question 1: What is Heron’s formula used for?

(A) Finding the area of a triangle
(B) Finding the perimeter of a triangle
(C) Finding the area of a rectangle
(D) Finding the volume of a triangle

Question 2: What is the semi-perimeter (s) of a triangle with sides 5 cm, 7 cm, and 8 cm?

(A) 9 cm
(B) 10 cm
(C) 11 cm
(D) 12 cm

Question 3: Heron’s formula for the area of a triangle is:

(A) A=s(s−a)(s−b)(s−c)
(B) A=21​×b×h
(C) A=s(s−a)(s−b)(s−c)​
(D) A=πr2

Question 4: A triangle has sides 6 cm, 8 cm, and 10 cm. What is its semi-perimeter?

(A) 10 cm
(B) 11 cm
(C) 9 cm
(D) 12 cm

Question 5: If a triangle has sides 3 cm, 4 cm, and 5 cm, what is its area using Heron’s formula?

(A) 5
(B) 6
(C) 7
(D) 8

Question 6: Which of the following is NOT required for Heron’s formula?

(A) Side lengths
(B) Semi-perimeter
(C) Height
(D) Triangle type

Question 7: A triangle has sides 13 cm, 14 cm, and 15 cm. What is its semi-perimeter?

(A) 20 cm
(B) 21 cm
(C) 22 cm
(D) 23 cm

Question 8: What is the first step in using Heron’s formula?

(A) Find the base and height
(B) Find the type of triangle
(C) Multiply all side lengths
(D) Calculate the semi-perimeter

Question 9: A triangle has sides 9 cm, 12 cm, and 15 cm. What is its area?

(A) 54 cm²
(B) 45 cm²
(C) 50 cm²
(D) 60 cm²

Question 10: Why is Heron’s formula useful?

(A) Only works for right triangles
(B) Requires angles to be known
(C) Works for any triangle when sides are known
(D) Only works for equilateral triangles