Finding Equilateral Triangle Area from Perimeter
To find the area of an equilateral triangle given its perimeter, we first need to determine the length of one side.
Calculating Side Length
An equilateral triangle has three equal sides. The perimeter is the total length of all sides.
- Given Perimeter = 24 cm
- Perimeter of an equilateral triangle = 3 × side length (s)
- Therefore, 24 cm = 3 × s
- Solving for s: s = 24 cm / 3 = 8 cm
The side length of the equilateral triangle is 8 cm.
Calculating Triangle Area
The formula for the area of an equilateral triangle is:
Area = $\frac{\sqrt{3}}{4} \times s^2$
- Substitute the side length (s = 8 cm) into the formula:
- Area = $\frac{\sqrt{3}}{4} \times (8 \text{ cm})^2$
- Area = $\frac{\sqrt{3}}{4} \times 64 \text{ cm}^2$
- Area = $16\sqrt{3} \text{ cm}^2$
The area of the equilateral triangle is $16\sqrt{3} \text{ cm}^2$.
Similar Questions
- The area of the greatest circle that can be inscribed inside a square of side 21cm is:
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- If the difference between the exterior and the interior angles of a regular polygon is $60^{\circ}$, with an interior angle being greater than the corresponding exterior angle, then find the number of sides of the polygon.
- 4 angles of a pentagon are $70^\circ$, $110^\circ$, $135^\circ$ and $95^\circ$. Find the measure of the fifth angle of the pentagon.
- If the perimeter of a square is 20 cm, then what is its area?
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- The length of a rectangular plot is twice its breadth and the length of its diagonal is $6\sqrt{5}$ m. The perimeter of the plot is ______.
- The length and the breadth of a rectangular park are in the ratio 7 : 3. The perimeter of the park is 21000 m. What is the difference between the length and the breadth of the park?
- What is the sum of the measures of the interior angles of a hexagon?
Important Questions from Plane Figures
If length of a rectangle is increased to its three times and breadth is decreased to its half, then the ratio of the area of given rectangle to the area of new rectangle is:
The width of the path around a square field is 4.5 m and its area is 105.75 m 2. Find the cost of fencing the field at the rate of Rs. 100 per meter.
What is the area of the square (in cm 2) whose vertices lie on a circle of radius 5 cm?
The circumcentre of an equilateral triangle is at a distance of 3.2 cm from the base of the triangle. What is the length (in cm) of each of its altitudes?
The perimeter of a circular lawn is 1232 m. There is 7 m wide path around the lawn. The area (in m 2) of the path is:
Take \(\left(\pi=\frac{22}{7}\right)\)
