You are told that it's a square base and the incline is 45 degrees.
So we can break this up into the sum of the areas of one square and four triangles.
The square is easy as we are given the length of the side of the square:
A = s²
A = 10²
A = 100 ft²
Now for the triangles, which is a little more tricky. The dashed line dropped down cuts one triangle into two identical right triangles.
The base is half of the original base length, so 5 ft. The height is unknown, which is what we are looking for. Then we know the opposite angle. So we can use tangents to determine the height as the known length is adjacent to the angle.
tan() = opp/adj
tan(45) = x / 5
The tangent of 45 degrees is 1, so:
1 = x / 5
x = 5
So the height is 5.
Now we know the height and base of the triangle, we can find the area of one, then multiply it by 4:
Answers & Comments
Verified answer
You are told that it's a square base and the incline is 45 degrees.
So we can break this up into the sum of the areas of one square and four triangles.
The square is easy as we are given the length of the side of the square:
A = s²
A = 10²
A = 100 ft²
Now for the triangles, which is a little more tricky. The dashed line dropped down cuts one triangle into two identical right triangles.
The base is half of the original base length, so 5 ft. The height is unknown, which is what we are looking for. Then we know the opposite angle. So we can use tangents to determine the height as the known length is adjacent to the angle.
tan() = opp/adj
tan(45) = x / 5
The tangent of 45 degrees is 1, so:
1 = x / 5
x = 5
So the height is 5.
Now we know the height and base of the triangle, we can find the area of one, then multiply it by 4:
A = bh/2
A = 10 * 5 / 2
A = 50 / 2
A = 25 ft²
times 4:
25 * 4 = 100 ft²
Add that to the area of the base:
100 + 100 = 200 ft²
Hope that helped. Best answer if it did.
IM SENT ME im sent me