A painter needs to cover a triangular region 63m by 66m by 73m. A can of paint covers 70squaremeters. How many cans will be needed
To find the total area of the triangular region, we can use Heron's formula.
Let's label the sides of the triangle as a, b, and c. Therefore, the sides are:
a = 63m
b = 66m
c = 73m
Using Heron's formula:
s = (a + b + c)/2
s = (63 + 66 + 73)/2
s = 101
Now, we can calculate the area of the triangle:
Area = √(s * (s-a) * (s-b) * (s-c))
Area = √(101 * (101-63) * (101-66) * (101-73))
Area ≈ √(101 * 38 * 35 * 28)
Area ≈ √(37127140)
Area ≈ 6091m^2
Now, we can calculate the number of cans needed:
Number of cans = Total area / Area covered per can
Number of cans = 6091 / 70
Number of cans ≈ 87.01
Therefore, the painter will need approximately 87 cans of paint to cover the triangular region.
To find the number of cans needed, we need to calculate the total area of the triangular region and then divide it by the area covered by one can of paint.
Step 1: Calculate the area of the triangular region using Heron's formula.
Let's consider the sides of the triangle as a = 63m, b = 66m, and c = 73m.
s = (a + b + c) / 2
s = (63 + 66 + 73) / 2 = 202 / 2 = 101
Area = √(s * (s - a) * (s - b) * (s - c))
Area = √(101 * (101 - 63) * (101 - 66) * (101 - 73))
Area = √(101 * 38 * 35 * 28)
Area ≈ √(3766600)
Area ≈ 1939.88648 square meters
Step 2: Divide the total area by the area covered by one can of paint.
Number of Cans = Area / Area covered by one can of paint
Number of Cans = 1939.88648 / 70
Number of Cans ≈ 27.712 specialized cans
Since we cannot buy a fraction of a can, the painter will need to buy 28 cans of paint to cover the triangular region.