A prism is a solid that has two parallel faces which are congruent polygons at both ends. These faces form the bases of the prism. A prism is named after the shape of its base. The other faces are in the shape of parallelograms. They are called lateral faces.The following diagrams show a triangular prism and a rectangular prism.
A right prism is a prism that has its bases perpendicular to its lateral surfaces.
When we cut a prism parallel to the base, we get a cross section of a prism. The cross section is congruent (same size and shape) as the base, as can be seen in the following diagram.
The surface area of a prism is the total area of all its external faces.
Step 1 :
Determine the shape of each face.
Step 2 : Calculate the area of each face.
Step 3 : Add up all the areas to get the total surface area.
We can also use the formula
Surface area of prism = 2 × area of base + perimeter of base × height
Worksheet to calculate the surface area and volume of a rectangular prism
Calculate the surface area of the following prism.
There are 2 triangles with the base = 4 cm and height = 3 cm.
Area of the 2 bases
= 12 cm2
1 rectangle with length = 7 cm and width = 5 cm
Area = lw = 7 × 5 = 35 cm2
1 rectangle with length = 7 cm and width 3 m
Area = lw = 7 × 3 = 21 cm2
1 rectangle with length = 7 cm and width 4 m
Area = lw = 7 × 4 = 28 cm2
The total surface area is 12 + 35 + 21 + 28 = 96 cm2We can also use the formula
The diagram shows a prism whose base is a trapezoid. The surface area of the trapezoidal prism is 72 cm2. Find the value of x.
There are 2 rectangles with length = 5 cm and width = 3 cm
Area = 2 × 5 × 3 = 30 cm2
There is one rectangle with length = 5 cm and width = 4 cm
Area = 5 × 4 = 20 cm2
There is one rectangle with length = 5 cm and width = 2 cm
Area = 5 × 2 = 10 cm2
There are two trapezoids.
Area = cm2 = 6x cm2
Sum of area
30 + 20 + 10 + 6x = 72
60 + 6x = 72
x = 2
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