Heron or Never: Semiperimeter Madness
Find the area of a triangle with sides 6.5 cm, 7.5 cm, and 8 cm.
24 cm²
The first step in using Heron’s formula is to calculate ________
Semi perimeter
Find the area of a triangle with sides 37.5 cm, 50 cm, and 62.5 cm.
937.5cm²
A triangle has sides 5, 12, and 13. Which shortcut explains why its area can be calculated without Heron’s formula?
A) Right-angled triangle property
B) Equilateral triangle formula
C) Isosceles triangle property
D) Scalene triangle theorem
A) Right-angled triangle property
Find the area of a triangle with sides 82.5 cm, 110 cm, and 137.5 cm.
4537.5cm²
The perimeter of a triangle is 30 cm. Two sides are 10 cm and 12 cm. Find its area.
24 root 5cm² is the area
The side is 8cm
A triangle has sides 7 cm, 8 cm, and 9 cm.
The semi-perimeter of the triangle is __________ cm.
s = __________ cm
s - a = __________ cm
s - b = __________ cm
s - c = __________cm
The area of the triangle is __________ cm²
12
12 – 7 = 5
12 – 8 = 4
12 – 9 = 3
12 root 5cm² is the area
The perimeter of a triangle is 36 cm.
The sides are 9 cm, 12 cm, and 15 cm.
Find the area using Heron’s formula.
54cm²
A triangle has sides 13 cm, 14 cm, 15 cm.
Semi-perimeter: ______ cm
s = __________ cm
s-a = __________ cm
s-b = __________ cm
s-c = __________
Area = __________cm²
8
7
6
84
The perimeter of a triangle is 30 cm.
Its sides measure 5 cm, 12 cm, and 13 cm.
Find the area of the triangle.
30cm²
A triangular park has sides in the ratio 3 : 4 : 5 and perimeter 24 m. Find its area.
24m²
For a fixed semi-perimeter, s, the triangle that gives the maximum area is:
A) Right-angled triangle
B) Equilateral triangle
C) Isosceles triangle
D) Scalene triangle
B) Equilateral triangle
The perimeter of a triangle is 30 cm and its sides are in the ratio 5 : 12 : 13. Find its area.
60cm²
A triangle has sides x + 1, x + 2, x + 3. Heron’s formula shows its area increases as:
A) x increases
B) x decreases
C) x = 0
D) x = 1
A) x increases
The sides of a triangle are in the ratio 5 : 12 : 13.
If the sides measure 10 cm, 24 cm, and 26 cm, find the area using Heron’s formula.
120cm²
The sides of a triangle are (x + 2), (x + 4), (x + 6) cm. If the area is 6 root 15 cm², find x .
x=4
Heron’s formula can be used to calculate the area of:
A) Any triangle with all three sides known
B) Only right-angled triangles
C) Only isosceles triangles
D) Only equilateral triangles
Answer: A) any triangle with all three sides known
A triangle has sides x + 2, x + 1, and x + 3.
If its area is 6 cm², find the value of x.
x = 2
Heron’s formula is particularly useful when:
A) The altitude is not given
B) The base is unknown
C) Only one side is known
D) Angles are known
Answer: A) the altitude is not given
A triangle has sides x + 4, x + 3, 2x.
If its area is 12 cm², find x.
x = 3
A triangle has sides 9 cm, 12 cm, 15 cm. Find its area using Heron’s formula.
54 cm²
4
Heron’s formula can be derived using:
A) Algebraic manipulation and Pythagoras theorem
B) Only base × height formula
C) Only sine law
D) Only cosine law
Answer: A) algebraic manipulation and Pythagoras theorem
A triangle has sides 8 cm, 10 cm, 12 cm. Find its area using Heron’s formula.
5 root 63 cm²
Which property of a triangle ensures that (s - a), (s - b), (s - c) is largest for a given semi-perimeter s?
A) All sides equal
B) Two sides equal
C) One side much longer than others
D) All sides different
Answer: A) all sides equal (equilateral)
A triangle has sides 7 cm, 8 cm, and 9 cm. Find its area using Heron’s formula.
12 root 5 cm²