A pencil holder shaped like a triangular prism is shown. The height of the prism is 12 centimeters.
What is the lateral surface area of the pencil holder in square centimeters?
the top is 10 cm the length is 12 cm and the right and left side is 7 cm
To find the lateral surface area of the triangular prism, we need to find the area of all three faces excluding the bases.
The top face, which is a triangle, has a base of 10 cm and a height of 12 cm. So, its area is (1/2) * 10 cm * 12 cm = 60 cm^2.
The right and left faces are rectangles, with a length of 12 cm and a height of 12 cm. The area of each rectangle is 12 cm * 12 cm = 144 cm^2. Since there are two identical rectangles, the total area for both faces is 2 * 144 cm^2 = 288 cm^2.
So, the lateral surface area of the pencil holder is 60 cm^2 + 288 cm^2 = 348 cm^2.