15 mm

Question

12 mm
10 mm
8 mm
What is the surface area of the rectangular pyramid

Answer 1

To calculate the surface area of a rectangular pyramid, you need to add the area of the base (in this case, a rectangle) to the area of the four triangular faces.

Given the dimensions of the base:
Length = 15 mm
Width = 12 mm

Calculate the area of the base:
Area = Length x Width
Area = 15 mm x 12 mm
Area = 180 mm^2

Now calculate the area of the triangular faces:
Since the pyramid is rectangular, the triangles will all be the same size.
To calculate the area of a triangle, you need the base and height.

The base of each triangle is the same as the width of the rectangle: 12 mm
The height can be calculated using the Pythagorean theorem:
Height = sqrt((15/2)^2 + 10^2)
Height = sqrt(112.25) ≈ 10.6 mm

Now calculate the area of one triangle:
Area = (1/2) x base x height
Area = (1/2) x 12 mm x 10.6 mm
Area ≈ 63.6 mm^2

Calculate the total surface area of the rectangular pyramid by adding the area of the base to the area of the four triangular faces:
Surface Area = Base Area + 4 x Triangle Area
Surface Area = 180 mm^2 + 4 x 63.6 mm^2
Surface Area = 180 mm^2 + 254.4 mm^2
Surface Area = 434.4 mm^2

Therefore, the surface area of the rectangular pyramid is 434.4 mm^2.