Using the numbers 10cm,10cm, 8cm, and 10cm, 6cm to solve the surface area of
the triangler prism.
To find the surface area of a triangular prism, we first need to find the area of the triangular bases and the three rectangular faces.
1. Area of the triangular bases:
The formula for the area of a triangle is A = (1/2) * base * height. For the triangular base of the prism with sides 10cm, 8cm, and 10cm, the height can be found using the Pythagorean theorem:
h^2 = 10^2 - (8/2)^2
h^2 = 100 - 16
h^2 = 84
h ≈ 9.17cm
Now, we can find the area of the triangular base:
A = (1/2) * 10cm * 9.17cm
A ≈ 45.83cm^2
Since there are two bases, the total area of the triangular bases is:
2 * 45.83cm^2 = 91.66cm^2.
2. Area of the rectangular faces:
The three rectangular faces of the prism have dimensions 10cm x 6cm, 8cm x 6cm, and 10cm x 6cm. The areas of these faces are:
(10cm * 6cm) + (8cm * 6cm) + (10cm * 6cm) = 60cm^2 + 48cm^2 + 60cm^2 = 168cm^2.
Therefore, the total surface area of the triangular prism is the sum of the areas of the bases and faces:
91.66cm^2 + 168cm^2 = 259.66cm^2.
The surface area of the triangular prism is approximately 259.66cm^2.