A painter needs to cover a triangular region 63 meters by 66 meters by 73 meters .A gallon of paint covers 70 square meters.How many gallons will be needed?
The first step is to find the area of the triangular region. We can use Heron's formula to calculate the area:
s = (63 + 66 + 73) / 2 = 101
area = √(101(101 - 63)(101 - 66)(101 - 73)) = 2016.39 square meters
Next, we need to determine how many gallons of paint we will need to cover this area. Since one gallon of paint covers 70 square meters, we can divide the total area by 70 to get the number of gallons needed:
2016.39 / 70 = 28.80 gallons
Therefore, the painter will need 28.80 gallons of paint to cover the triangular region.
To find out how many gallons of paint will be needed, we need to calculate the total area of the triangular region and then divide it by the coverage area of one gallon of paint.
The triangular region has three sides measuring 63 meters, 66 meters, and 73 meters. To find the area of a triangle, we can use Heron's formula.
Let's calculate the semi-perimeter of the triangle first:
s = (a + b + c) / 2
s = (63 + 66 + 73) / 2
s = 201 / 2
s = 100.5
Using Heron's formula, we can find the area of the triangle:
Area = √(s * (s - a) * (s - b) * (s - c))
Area = √(100.5 * (100.5 - 63) * (100.5 - 66) * (100.5 - 73))
Area ≈ √(100.5 * 37.5 * 34.5 * 27.5)
Area ≈ √(4,864,218.75)
Area ≈ 2,204.96 square meters (rounded to two decimal places)
Now, we divide the total area by the coverage area of one gallon of paint to find the number of gallons needed:
Number of gallons = Total area / Coverage area of one gallon
Number of gallons = 2,204.96 / 70
Number of gallons ≈ 31.50 gallons (rounded to two decimal places)
Therefore, the painter will need approximately 31.50 gallons of paint to cover the triangular region.