Gerrad is a painter. he is using a canvas that is in the shape of a regular hexagon. The perimeter of the canvas is 78 in. The perpendicular distance from a side to the center is 11 in. to the nearest inch. Based on these measurements, what is area of the canvas
Divide the canvas into 6 isosceles triangles.
Base of triangle = 78/6=13"
Height of triangle = 11"
Area of each triangle = 11*13/2
Total area of canvas=11*13/2*6=432 sq.in.
Divide the canvas into 6 isosceles triangles.
Base of triangle = 78/6=13"
Height of triangle = 11"
Area of each triangle = 11*13/2
Total area of canvas=11*13/2*6=429 sq.in.
156
To find the area of the canvas, we need to determine the length of one side of the regular hexagon. We can then use this length to calculate the area.
Let's start by finding the length of one side of the hexagon. Since the hexagon has six equal sides, we can divide the perimeter by 6 to get the length of one side.
Perimeter of the hexagon = 78 in
Length of one side = Perimeter / 6
Length of one side = 78 in / 6 = 13 in
Now, we know the length of one side of the hexagon is 13 inches.
To find the area of a regular hexagon, we can use the formula:
Area = (3 * √3 * side length^2) / 2
Substituting the value of the side length into the formula, we have:
Area = (3 * √3 * 13^2) / 2
Now, we can calculate the area:
Area = (3 * √3 * 169) / 2
Area ≈ 1953.52 square inches (to the nearest inch)
Therefore, the area of the canvas is approximately 1953 square inches.