Area of an Equilateral Triangle

Q. The perimeter of an equilateral triangle is 36 cm. The area of the triangle is equal to

1. $24\sqrt{3}{\text{cm}}^2$
2. $36{\text{cm}}^2$
3. $36\sqrt{3}{\text{cm}}^2$
4. $24\sqrt{2}{\text{cm}}^2$

Q. If the area of an equilateral triangle is$20\sqrt{3}c{m}^2,$ then its perimeter is

1. 
   $12\sqrt{5}cm$
2. 
   $6\sqrt{5}cm$
3. 
   $8\sqrt{5}cm$
4. 
   $4\sqrt{5}cm$

Q.

The area of an equilateral triangle whose side is 2 cm is $\sqrt{A}$. The integral value of A is___

Q.

A square whose diagonal is $10cm$ long has an area equal to

Q. If the perimeter of an equilateral triangle is 60 cm, then its area is 1732 $c{m}^2$.

1. False
2. True

Q.

The sides of an equilateral triangle are (2a - b + 5), (a + b) and (2b - a + 2). What is the area of the triangle?

1. $\frac{\sqrt{3}}{4}\times a^2$

2. $\frac{\sqrt{3}}{4}\times b^2$

3. $\frac{\sqrt{3}}{4}\times 49$

4. $\frac{\sqrt{3}}{4}\times 81$

Q. A square and an equilateral triangle have equal perimeters. If the diagonal of the square is $12\sqrt{2}cm$, then the area of the triangle is:

1. $24\sqrt{2}c{m}^2$
2. $24\sqrt{3}c{m}^2$
3. $48\sqrt{3}c{m}^2$
4. $64\sqrt{3}c{m}^2$

Q. The area of a regular hexagon of side 4 cm is

1. $16\sqrt{3}c{m}^2$
2. $12\sqrt{3}c{m}^2$
3. $24\sqrt{3}c{m}^2$
4. $4\sqrt{3}c{m}^2$

Q. If the area of an equilateral triangle is $36\sqrt{3}c{m}^2$, Then find the perimeter of the triangle is

1. 
   24 cm
2. 
   36 cm
3. 
   12 cm
4. 
   38 cm

Q. If the area of an equilateral triangle is $16\sqrt{3}c{m}^2$, then the perimeter of the triangle is
(3 Marks)

Q. Which of the following statements is true?

1. We can find the area of a triangle if we know two of the sides of the triangle.
2. We can find the area of a triangle if we know all the sides of the triangle.
3. We can find the area of a triangle if we know two of the angles of the triangle.
4. We can find the area of a triangle if we know all the angles of the triangle.