Worksheet on Area of Equilateral Triangle

Three equal sides create perfectly balanced triangular spaces. Mathematics enthusiasts explore printable areas of equilateral triangle practice questions that unlock the secrets of calculating space within these special geometric shapes. These engaging exercises teach students the unique formula for equilateral triangles while connecting geometry to real-world applications. Students can download a free area of equilateral triangle worksheet PDF; every calculation builds spatial reasoning and mathematical confidence.

1. What is the area of an equilateral triangle with a side length of 12 cm?

a) 18√3 cm²
b) 16√3 cm²
c) 144√3 cm²
d) 36√3 cm²

Answer: d)

Explanation: Formula used: Area of an equilateral triangle = $\frac{\sqrt{3}{}^{}}{4}$ a²
Where a: side of an equilateral triangle
Substituting the side in the formula, we get
Area of an equilateral triangle = $\frac{\sqrt{3}{}^{}}{4}$ x 12²
                                                 = $\frac{\sqrt{3}{}^{}}{4}$ x 144
                                                 = 36√3 cm²

2. Calculate the side length of an equilateral triangle whose area is 72√3 square metres.

a) √2 cm
b) 12 cm
c) 6√2 cm
d) 36√2

Answer: a)

Explanation: Area of an equilateral triangle = $\frac{\sqrt{3}{}^{}}{4}$ a²
Substituting the area in the formula, we get
72√3 = $\frac{\sqrt{3}{}^{}}{4}$ a²
On solving, a = 12√2 cm

3. The perimeter of an equilateral triangle is 18 cm. What is the area of the triangle?

a) 27√3 cm²
b) 36 cm²
c) 9√3 cm²
d) 2√3 cm²

Answer: c)

Explanation: Each side of the triangle = 18/3 = 6 cm.
Using the area formula: A = $\frac{\sqrt{3}{}^{}}{4}$ a²
                                          = $\frac{\sqrt{3}{}^{}}{4}$ x 6 x 6
                                          = 9√3 square units

4. What is the perimeter of an equilateral triangle if its area is 4√3 square units?

a) 16 units
b) 12 units
c) 6 units
d) 4 units

Answer: b)

Explanation: Area of an equilateral triangle = $\frac{\sqrt{3}{}^{}}{4}$ a²
4√3 = $\frac{\sqrt{3}{}^{}}{4}$ a²
On solving, we will get
a = 4 units
So, the side of an equilateral triangle = 4 units

Now, perimeter of an equilateral triangle = 3a
                                                                  = 3 x 4
                                                                  = 12 units

5. What is the radius of the circumcircle of an equilateral triangle with a side length of 14 cm?

a) 7 cm
b) 7√3 cm
c) 14√3 cm
d) 14/√3 cm

Answer: d)

Explanation: The radius r of the circumcircle of an equilateral triangle is given by
r = $\frac{\mathrm{s}{}^{}}{\sqrt{3}}$ where s is the side of the triangle
Putting the value s = 14 units, we will get
r = $\frac{14{}^{}}{\sqrt{3}}$ units

6. How does the area change if the side length of an equilateral triangle is doubled?

a) The area doubles.
b) The area triples.
c) The area increases by 4 times.
d) The area increases by six times.

Answer: c)

Explanation: let the side of an equilateral triangle be ‘s’
New side = 2s
New area = $\frac{\sqrt{3}{}^{}}{4}$ (2s)²
              = √3 s²
We can also write it as 4 x $\frac{\sqrt{3}{}^{}}{4}$ s².

Thus, the area increases by 4 times.

7. If the side length of an equilateral triangle is 6 cm, what is its area? (Use √3 = 1.732)

a) 36 cm²
b) 30 cm²
c) 15.588 cm²
d) 17.45 cm²

Answer: c)

Explanation: Area of an equilateral triangle = $\frac{\sqrt{3}{}^{}}{4}$ a²
                                                                        = $\frac{\sqrt{3}{}^{}}{4}$ x 6²
                                                                        = $\frac{\frac{\mathrm{1.732}}{}}{\frac{4}{}}$x 36 (since 1.732)
                                                                        = 15.588 cm²

8. If the height of an equilateral triangle is 9 cm, what is its area?

a) 27√3 cm²
b) 40.5 cm²
c) 54√3 cm²
d) 81 cm²

Answer: a)

Explanation:
The formula for the height of an equilateral triangle is:
h = $\frac{\mathrm{s}\sqrt{3}{}^{}}{4}$
where s: side of an equilateral triangle
h: height of an equilateral triangle.
9 = $\frac{\mathrm{s}\sqrt{3}{}^{}}{4}$
On solving, s = 6√3 cm
Now, using the formula for the area of an equilateral triangle:
A = $\frac{\sqrt{3}{}^{}}{4}$ a²
   = $\frac{\sqrt{3}{}^{}}{4}$ x 6√3 x 6√3
   = 27√3 cm²

9. An equilateral triangle has an area of 25√3 cm². What is its perimeter?

a) 15 cm
b) 45 cm
c) 30 cm
d) 50 cm

Answer: c)

Explanation: Using the formula of the area of an equilateral triangle = $\frac{\sqrt{3}{}^{}}{4}$ a²
25√3 = $\frac{\sqrt{3}{}^{}}{4}$ a²
On solving a = 10 cm
The perimeter of an equilateral triangle = 3a
                                                         = 3  x 10
                                                         = 30 cm

10. An equilateral triangle and a square have the same perimeter. If the area of the square is 36 cm², what is the area of the triangle?

a) 16 cm²
b) 32 cm²
c) 16√3 cm²
d) 16/√3 cm²

Answer: c)

Explanation: Area of the square = s² where s: side of the square
36 = s²
s = 6 cm
The perimeter of the square = 4s = 4 x 6 = 24 cm
It is given that the perimeter of an equilateral triangle is the same as that of a square.

Let the side of an equilateral triangle be a.
The perimeter of an equilateral triangle = 3a
Since the perimeter of an equilateral triangle is the same as that of a square,
                                                          24 = 3a

On solving, a = 8 cm

Now, finding the area of the triangle:
A = $\frac{\sqrt{3}{}^{}}{4}$ a²
   = $\frac{\sqrt{3}{}^{}}{4}$ (8)²
   = $\frac{\sqrt{3}{}^{}}{4}$ x 64
   = 16√3 cm²