A painter needs to cover a triangular region 63 m by 66 m by 73 m.A can of paint covers 70 square meters. How many cans will be needed?
by Heron's Formula
s = (1/2)perimeter
= (1/2)(63+66+73) = 101
s-a = 101-63 = 38
s-b = 101-66 = 35
s-c = 101-73 = 28
area = √(s(s-a)(s-b)(s-c) )
= √(101*38*35*28) = appr 1939.39 m^2
or, find the acute angle opposite side 63
63^2 = 66^2 + 73^2 - 2(66)(73)cos A
cosA = .59319...
angle A = 53.616135
area = (1/2)(66)(73)sin53.616135 = 1939.39 m^2, same as above
number of cans = 1939.39/70 = 27.71 cans
the painter will need 28 cans, (how do you buy .71 of a can ?)
Assessment questions
What is the answer
Well, it looks like the painter has a colorful challenge ahead. Since the triangular region has three sides of lengths 63 m, 66 m, and 73 m, we can use the Heron's formula to find the area of the triangle. However, my expertise lies in making people laugh, not mathematical equations. So let me tell you a joke instead:
Why don't scientists trust atoms? Because they make up everything!
I hope that brought a smile to your face, but for the actual answer to your question, you need to calculate the area of the triangle and divide it by the coverage of one can of paint (70 square meters). Good luck with your painting project!
To find out how many cans of paint will be needed to cover the triangular region, we first need to calculate its area.
Since the given dimensions are for a triangle, we can use Heron's formula to find the area. The formula states that the area of a triangle with side lengths a, b, and c can be calculated using the following formula:
Area = √(s(s-a)(s-b)(s-c))
Where s is the semi-perimeter of the triangle, calculated as:
s = (a + b + c) / 2
Let's calculate the semi-perimeter s first:
s = (63 + 66 + 73) / 2
s = 201 / 2
s = 100.5
Now, we can calculate the area of the triangle using Heron's formula:
Area = √(100.5(100.5-63)(100.5-66)(100.5-73))
Area ≈ √(100.5 * 37.5 * 34.5 * 27.5)
Area ≈ √(875296.875)
Area ≈ 935.414 square meters (rounded to three decimal places)
Now that we know the area of the triangular region is approximately 935.414 square meters, we can calculate the number of cans needed.
Given that each can of paint covers 70 square meters, we divide the total area by the coverage area of a can:
Number of cans = Area / Coverage area per can
Number of cans = 935.414 / 70
Number of cans ≈ 13.364
Since we can't have a fraction of a can, we need to round up to the nearest whole number.
Therefore, the painter will need approximately 14 cans of paint to cover the triangular region.