A triangular flower garden measure 10m, 15m and 24m. find the area of the garden
s = (1/2)(49) = 49/2
s-a = 49/2 - 20/2= 29/2
s-b = 49/2 - 30/2 = 19/2
s-c = 49/2 - 48/2 = 1/2
product = (1/16)( 26999)
sqrt of product = (1/4)(164.3)
= 41.08
well, there is an easy way but it is not commonly used, Huron's fomula.
if s = (1/2) (a+b+c)
then Area = sqrt [ s (s-a)(s-b)(s-c) ]
To find the area of a triangular garden, we can use Heron's formula.
Heron's formula states that the area of a triangle with side lengths a, b, and c is given by:
Area = √(s(s-a)(s-b)(s-c))
where s is the semi-perimeter of the triangle, which is calculated as:
s = (a + b + c) / 2
In this case, the side lengths of the triangular garden are given as 10m, 15m, and 24m.
Let's calculate the area step by step:
Step 1: Calculate the semi-perimeter (s)
s = (10 + 15 + 24) / 2
s = 49 / 2
s = 24.5
Step 2: Calculate the area
Area = √(24.5(24.5-10)(24.5-15)(24.5-24))
Area = √(24.5 * 14.5 * 9.5 * 0.5)
Area = √(12654.125)
Area ≈ 112.51 m²
Therefore, the area of the triangular flower garden is approximately 112.51 square meters.
To find the area of a triangular flower garden, we can use the formula for the area of a triangle, which is given by:
Area = (Base * Height) / 2
In this case, we need to determine the base and height of the triangle.
The base of the triangle can be any one of its sides. Let's choose one side as the base.
Now, to find the height, we need to draw an altitude from the opposite vertex to the base. An altitude is a perpendicular line segment from a vertex to the base.
Let's assume that the base of the triangle is the side measuring 10m.
To find the height, we can consider the triangle formed by the sides measuring 10m, 15m, and 24m.
This triangle is a right triangle since the sum of the squares of the two shorter sides (10m and 15m) is equal to the square of the longest side (24m).
To find the height, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the hypotenuse is the side measuring 24m, and the other two sides are 10m and 15m.
So, using the Pythagorean theorem, we have:
24^2 = 10^2 + 15^2
576 = 100 + 225
576 = 325
Taking the square root of both sides, we find:
√576 = √325
24 = √325
Now we have found the height, which is 24m.
We can substitute the base and height into the area formula:
Area = (Base * Height) / 2
Area = (10m * 24m) / 2
Calculating this equation gives us:
Area = (240m^2) / 2
Area = 120m^2
Therefore, the area of the triangular flower garden is 120 square meters.