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
Height= 12cm base = 7cm width=10cm
To find the lateral surface area of the triangular prism, we need to calculate the area of the three rectangular faces.
The first rectangular face has a length equal to the height of the prism (12 cm) and a width equal to the base of the prism (7 cm). Therefore, the area of this face is 12 cm x 7 cm = 84 cm^2.
The other two rectangular faces have the same dimensions. The width is still 7 cm, but the length is equal to the width of the triangular base of the prism (10 cm). Therefore, the area of each of these faces is 7 cm x 10 cm = 70 cm^2.
Since there are three rectangular faces in total, we multiply the area of each face by 3 to get the total lateral surface area.
Total lateral surface area = (84 cm^2 + 70 cm^2 + 70 cm^2) x 3 = 594 cm^2.
Thus, the lateral surface area of the pencil holder is 594 square centimeters.