Find the Surface Area of the Rectangular Pyramid.
Length = 6
Width = 6
Height = 13
Slant Height = 13.3
Show Work.
(This is 10th grade math, please don't make advanced)
The surface area of a rectangular pyramid is given by:
SA = L*W + L*sqrt((h^2)+(s^2))/2 + W*sqrt((h^2)+(s^2))/2
where L and W are the length and width of the rectangle base, h is the height of the pyramid, and s is the slant height.
Plugging in the values:
SA = 6*6 + 6*sqrt((13^2)+(13.3^2))/2 + 6*sqrt((13^2)+(13.3^2))/2
SA = 36 + 6*sqrt(344.89)/2 + 6*sqrt(344.89)/2
SA = 36 + 39.39 + 39.39
SA = 114.78
Therefore, the surface area of the rectangular pyramid is approximately 114.78 square units.
To find the surface area of a rectangular pyramid, we need to calculate the areas of its base and its four triangular faces.
The base of the rectangular pyramid is a rectangle with length 6 and width 6. Therefore, the area of the base is given by:
Area of base = length × width = 6 × 6 = 36 square units.
Next, let's calculate the areas of the four triangular faces.
The slant height of each triangular face is given as 13.3, and the height of the pyramid is 13. As the slant height, height, and base of each triangular face form a right-angled triangle, we can find the length of the base of each triangular face using the Pythagorean theorem:
(base of triangular face)^2 + (height of triangular face)^2 = (slant height)^2.
Let's calculate the base for one of the triangular faces:
(base of triangular face)^2 + 13^2 = 13.3^2.
(base of triangular face)^2 + 169 = 176.89.
(base of triangular face)^2 = 7.89.
base of triangular face = √7.89 ≈ 2.81.
Now we can calculate the area of one triangular face:
Area of triangular face = ½ × base × height
= ½ × 2.81 × 13
≈ 18.29 square units.
Since we have four triangular faces, the total surface area of the rectangular pyramid is:
Total surface area = area of base + 4 × area of triangular face
= 36 + 4 × 18.29
= 36 + 73.16
= 109.16 square units.
Therefore, the surface area of the rectangular pyramid is approximately 109.16 square units.