Find the area of an equilateral triangle whose base is 10 cm.
2 right angled triangles = 1 equilateral triangle. You can pretty much split it down the middle and you'll see the 2 triangles from.
The formula for a right angle triangle is:
(b x h)/2 = area
If we were solving for 1/2 the triangle we know that the base is 5 cm, the height is unknown and the hypotenuse is 10 cm.
Using Pythagorean theorem we can solve for the height:
a^2 + b^2 = c^2
5^2 + b^2 = 10^2
25 + b^2 = 100
b^2 = 75
b = about 8.66
Now we can plug this value for our height back into the equation:
(b x h)/2 = area
(5 x 8.66)/2 = area
21.65 cm^2
Remember this is only 1/2 of the triangle so you could multiple by 2 (or simply do not divide my 2 in the above equation):
Area of equilateral triangle = 43.30 cm^2
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To find the area of an equilateral triangle, you need to know the length of one side. In this case, the base of the triangle is given as 10 cm.
Step 1: Find the length of one side.
In an equilateral triangle, all sides are equal. Since the base is 10 cm, all sides of the triangle will also be 10 cm.
Step 2: Use the formula for the area of an equilateral triangle.
The formula to find the area of an equilateral triangle is:
Area = (√3 / 4) * (side length)^2
Substituting the value of the side length, we have:
Area = (√3 / 4) * (10 cm)^2
Step 3: Evaluate the expression.
Area = (√3 / 4) * 100 cm^2
Area = (√3 * 100) / 4 cm^2
Area = (√300) / 4 cm^2
Step 4: Simplify the radical.
To simplify the radical, you can express √300 as √(100 × 3).
Area = (10√3) / 4 cm^2
Area ≈ 2.58 cm^2 (rounded to two decimal places)
Therefore, the area of the equilateral triangle is approximately 2.58 cm^2.
To find the area of an equilateral triangle, you can use the formula:
Area = (sqrt(3) / 4) * s^2,
where s is the length of each side of the triangle.
In an equilateral triangle, all sides are equal. Given that the base of the equilateral triangle is 10 cm, we know that each side is also 10 cm.
So, plugging in the value of s = 10 cm, we can calculate the area.
Area = (sqrt(3) / 4) * 10^2
= (sqrt(3) / 4) * 100
= (1.732 / 4) * 100
= 0.433 * 100
= 43.3 cm²
Therefore, the area of the equilateral triangle is 43.3 square centimeters.