Area of an Equilateral Triangle

Q.

One side of an equilateral triangle measures $\text{8 cm}$. Find its area using Herons formula. What is its altitude?

Q.

Find the area of the equilateral triangle given below:

Given: AD=10 cm.

1. 20 tiles

2. 25 tiles

3. 35 tiles

4. 50 tiles

Q. The area of an equilateral triangle of side $\text{8 cm}$ is ${cm}^2$.

1. $6\sqrt{3}$
2. $16\sqrt{3}$
3. $16\sqrt{5}$

Q.

Derive the formula for height and area of an equilateral triangle

Q.

If ‘a’ is the side of an equilateral triangle and ‘h’ is the height, which of the following expressions can be used to find the area of the triangle?

1. $\frac{1}{2}$ $\times$ a $\times$ h

2. a $\times$ h

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

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

1. 1 and 3
2. 1 and 4
3. 2 and 3
4. 2 and 4

Q.

A caution sign is shown in the given figure. It consists of two equilateral triangles. Find the area of the region painted in red. [Use $\sqrt{3}=1.732$]

1. $443.4c{m}^2$

2. $440.4c{m}^2$

3. $438.4c{m}^2$

4. None of these

Q. How to find the altitude of a triangle if the area and base are given.

Q.

A hexagonal field of side 30 m has to be used for playing cricket. Find its area.

1. 387.74 m²

2. 487.74 m²

3. 587. 74 m²

4. 667.6 m²

Q. Area of each small square is $1c{m}^2$. So, what is the area of red triangle?

1. $20c{m}^2$
2. $10c{m}^2$
3. $15c{m}^2$
4. $1c{m}^2$

Q. Prove that area of an equilateral triangle formed any side of a square is half the area of an equilateral triangle formed at the diagonal of same square.

Q. A metal wire, when bent in the form of an equilateral triangles of largest area, encloses an area of $484\sqrt{3}c{m}^2$. If the same wire is bent into the form of a circle of largest area, find the area of this circle.

1. 4772 $c{m}^2$
2. 2597 $c{m}^2$
3. 1386 $c{m}^2$
4. 1126 $c{m}^2$