The shapes side is 10 cm the shapes side is 10 cm the bottom of the shape is 10 cm the front of the shape is 8 cm the bottom of the shape is 6 cm Solve for the surface area of the triangular prism.
(1 point)
A. 260 square centimeters
B. 180 square centimeters
C. 280 square centimeters
D. 320 square centimeters
To solve for the surface area of the triangular prism, we need to calculate the areas of each individual face and sum them up.
Front and back faces: The front face is a triangle with a base of 10 cm and a height of 8 cm. The area is (1/2)*base*height = (1/2)*10*8 = 40 square cm. Since there are two front and back faces, the total area is 2*40 = 80 square cm.
Top and bottom faces: The top face is a triangle with a base of 6 cm and a height of 8 cm. The area is (1/2)*base*height = (1/2)*6*8 = 24 square cm. Again, there are two top and bottom faces, so the total area is 2*24 = 48 square cm.
Side faces: The side faces are rectangles with sides of 10 cm and 8 cm. The area of each side face is length*width = 10*8 = 80 square cm. Since there are two side faces, the total area of the side faces is 2*80 = 160 square cm.
Therefore, the total surface area of the triangular prism is 80 + 48 + 160 = 288 square cm.
The closest option is C. 280 square centimeters.