Equilateral Triangle Calculations
This problem requires finding the area and altitude of an equilateral triangle with a given side length.
Area Calculation
The formula for the area of an equilateral triangle with side length '$a$' is:
$ \text{Area} = \frac{\sqrt{3}}{4} a^2 $
Given the side length '$a = 2$ cm':
- Substitute the side length into the formula:
$ \text{Area} = \frac{\sqrt{3}}{4} (2 \text{ cm})^2 $
- Simplify the expression:
$ \text{Area} = \frac{\sqrt{3}}{4} \times 4 \text{ cm}^2 $
$ \text{Area} = \sqrt{3} \text{ cm}^2 $
Altitude Calculation
The formula for the altitude (height) '$h$' of an equilateral triangle with side length '$a$' is:
$ h = \frac{\sqrt{3}}{2} a $
Given the side length '$a = 2$ cm':
- Substitute the side length into the formula:
$ h = \frac{\sqrt{3}}{2} (2 \text{ cm}) $
- Simplify the expression:
$ h = \sqrt{3} \text{ cm} $
Final Result
The calculated area is $\sqrt{3} \text{ cm}^2$ and the altitude is $\sqrt{3} \text{ cm}$.
Similar Questions
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Important Questions from Geometry
If the angles of a triangle are in the ratio of 2:3:4, then the difference of the measure of greatest angle and smallest angle is
In ΔABC, ∠A = 90°, AD ┴ BC and AD = BD = 2 cm. The length of CD is
How many lines of symmetry does a rectangle have?
The number of diagonals in each face a cube is
Which of the following is/are the geometric figures with the line of symmetry?
I. Rectangle
II. Isosceles triangle
