The Surface Area of a Square Pyramid is 112 sq. ft. If the Length of Each Edge of the Base is 8 ft, what is the Height of each Triangular Face?
Total surface area = 112 sq.ft
area of base = 8²=64 sq. ft
Area of 4 slant faces = 112-64 = 48 sq.ft
Area of each slant face = 48/4=12 sq. ft
base of slant face = 8
Let H=height of slant face
8*H/2=12 sq.ft
H=3 ft.
Why did the pyramid go to school?
To learn how to calculate its height, of course!
Now, let's crack this math problem with a smile.
The surface area of a square pyramid is given by the formula:
S = L^2 + 2Lh
Where:
S is the surface area
L is the length of each edge of the base
h is the height of each triangular face
In this case, S = 112 sq. ft. and L = 8 ft.
Let's plug these values into the equation and solve for h. Ready? Here we go:
112 = 8^2 + 2(8)h
112 = 64 + 16h
48 = 16h
h = 48/16
h = 3 ft
Ta-da! The height of each triangular face is 3 feet. Hope this answer made you pyramid with laughter!
To find the height of each triangular face of a square pyramid, we can use the formula:
Surface Area = Base Area + Lateral Area
Surface Area of a square pyramid = Base Area + (Perimeter of Base × Height of Each Triangular Face)
Given that the Surface Area is 112 square feet and the length of each edge of the base is 8 feet, we can calculate the height of each triangular face.
Step 1: Calculate the Base Area
The base of a square pyramid is a square, and the area of a square is given by the formula: Area = side^2.
Therefore, the Base Area = (8 ft)^2 = 64 sq. ft.
Step 2: Calculate the Perimeter of the Base
Since the base is a square, all four sides are equal. So, the perimeter of the base = 4 × side = 4 × 8 ft = 32 ft.
Step 3: Calculate the Lateral Area
Lateral Area = Surface Area - Base Area
Using the given Surface Area of 112 sq. ft and the calculated Base Area of 64 sq. ft, we get:
Lateral Area = 112 sq. ft - 64 sq. ft = 48 sq. ft.
Step 4: Substitute values into the formula to find the height of each triangular face:
Lateral Area = (Perimeter of Base × Height of Each Triangular Face)
48 sq. ft = 32 ft × Height of Each Triangular Face
Step 5: Solve for the Height of Each Triangular Face:
Height of Each Triangular Face = (48 sq. ft) ÷ (32 ft) = 1.5 ft.
Therefore, the height of each triangular face of the square pyramid is 1.5 feet.
To find the height of each triangular face of a square pyramid, we can use the formula for the surface area of a square pyramid and substitute the given values.
The formula for the surface area of a square pyramid is:
Surface Area = Base Area + 4 * (0.5 * base edge length * height)
Let's substitute the given values into the formula:
112 sq. ft. = Base Area + 4 * (0.5 * 8 ft * height)
To find the base area, we need to find the area of a square with an edge length of 8 ft.
Base Area = edge length * edge length
Base Area = 8 ft * 8 ft
Base Area = 64 sq. ft.
Now let's substitute the values into the formula again:
112 sq. ft. = 64 sq. ft. + 4 * (0.5 * 8 ft * height)
Now, let's simplify the equation:
48 sq. ft. = 4 * 4 ft * height
Simplifying further:
48 sq. ft. = 16 ft * height
Divide both sides of the equation by 16 ft:
3 ft = height
Therefore, the height of each triangular face of the square pyramid is 3 ft.