The surface area of the triangular prism is 686.6 cm².
Step-by-step explanation:
Step 1:
The volume of a triangular prism can be determined by multiplying its area of the triangular base with the length of the prism.
The base triangle has a base length of 10 cm and assume it has a height of h m.
The volume of the prism[tex]= \frac{1}{2} (b)(h) (length) = \frac{1}{2} (10)(h)(20) = 866.[/tex]
[tex]h = \frac{866(2)}{10(20)} = 8.66.[/tex]
The height of the triangle is 8.66 cm.
Step 2:
The surface area of the triangle is obtained by adding all the areas of the shapes in the prism. There are 2 triangles and 3 rectangles in a triangular prism.
The triangles have a base length of 10 cm and a height of 8.66 cm. A triangles area is half the product of its base length and height.
The rectangles all have a length of 20 cm and a width of 10 cm. The area of a rectangle is the product of its length and width.
The area of the 2 triangles [tex]= 2 [\frac{1}{2} (10)(8.66)] = 86.6.[/tex]
The area of the 3 rectangle [tex]= 3[(20)(10)] = 600.[/tex]
Step 3:
The surface area of the triangular prism [tex]= 86.6 + 600 = 686.6.[/tex]
The surface area of the prism is 686.6 cm².
