Determine the area of the triangular base of the prism.
Determine the area of the smallest rectangle of the prism
. Determine the area of the largest rectangle of the prism.
What is the total surface area of the triangular prism?
DIMENSIONS
6cm
4cm
7cm
7cm
12cm
To calculate the area of the triangular base of the prism, we use the formula for the area of a triangle: 1/2 * base * height. The base is 6 cm and the height is 4 cm.
Area of triangular base = 1/2 * 6 cm * 4 cm = 12 cm^2
To calculate the area of the smallest rectangle of the prism, we use the formula for the area of a rectangle: length * width. The smallest rectangle is a face of the prism with dimensions 4 cm and 7 cm.
Area of smallest rectangle = 4 cm * 7 cm = 28 cm^2
To calculate the area of the largest rectangle of the prism, we use the same formula: length * width. The largest rectangle is the opposite face of the prism, with dimensions 6 cm and 7 cm.
Area of largest rectangle = 6 cm * 7 cm = 42 cm^2
To find the total surface area of the triangular prism, we need to calculate the areas of all the faces and then add them together. The prism has 2 triangular faces and 3 rectangular faces.
Total surface area = (2 * 12 cm^2) + 28 cm^2 + 42 cm^2 + 28 cm^2 + 42 cm^2 = 164 cm^2
Therefore, the total surface area of the triangular prism is 164 cm^2.