The shape is an irregular shape consisting of a triangular prism and cuboids. The volume is 232 cubic centimeters while the surface area is 234 centimeters square.
How do you calculate the volume of the Prism?
The shape can be dissected into three geometrical shapes:
Two cuboids and a prism.
The volume of a cuboid is given as follows:
Length x width x height.
Solving for the first cuboid, we have the following information:
Lenght = 3cm
Width = 8cm
Height = 5 cm
hence the volume is: 3 x 8 x 5 = 120cm
Solving for the second cuboid, we have the following information:
Lenght = 4cm
Width = 8cm, and
height = 2cm
Hence it's volume is given as: 4 x 8 x 2 = 64cm.
The formula for the volume of a triangular prism is given:
V = B * h, where B is the area of the triangular base.
First lets solve for B. This is given as:
1/2b*h where the Height (h) of the triangle is 3cm, and the base is 4cm.
Hence B = 1/2 * 3 * 4 = 6cm
hence the volume of the triangular prism is = 6 * 8 = 48cm
Hence the total volume of the shape is:
120 + 64 + 48 = 232cm³
To get the surface areas fo the shape, all that is required is to use the rudimentary formulas of lenght x breadth for each side that resembles a polygon.
This gives us: the respective surface areas:
29 + 29 + 40 + 16 + 24 + 56 + 40 = 234cm²
Learn more about irregular shapes at:
https://brainly.com/question/12704929
