A third 3-dimensional figure that you will encounter is a pyramid. Recall that a pyramid has only one polygon-shaped base, and the lateral faces are triangles instead of parallelograms or rectangles, like the lateral faces of a prism.

Pyramids are also named by the shape of their base. A triangular pyramid has a base in the shape of a triangle, a square pyramid has a base in the shape of a square, and a rectangular pyramid has a base in the shape of a rectangle.

Figure showing a triangular pyramid, square pyramid, and a rectangular pyramid, with a callout pointing out the shape of each pyramid's base

The Westmoreland Junior High 8th Grade Spring Dance has the theme, A Night on the Nile. The school cafeteria will be decorated in an Egyptian theme. The centerpiece will be a large square pyramid.

Pyramid with dimensions labeled

Interactive exercise. Assistance may be required. The class president wants to know the lateral surface area of the pyramid. Drag the dimensions from the Dimensions Box onto the appropriate place in the formula to calculate the lateral surface area of the pyramid. Use the formula, S = 1 over 2 1 2Pl


Now that you have correctly identified the dimensions, calculate the lateral surface area of the pyramid.

Interactive popup. Assistance may be required.

Check Your Answer

576 square feetClose Pop Up

Interactive exercise. Assistance may be required. The 8th grade class vice president has decided that the entire pyramid should be a canvas tent, and the floor of the pyramid should also be lined with canvas. Drag the dimensions from the Dimensions Box onto the appropriate place in the formula to calculate the total surface area of the pyramid. Use the formula, S = 1 over 2 1 2Pl + B


Now that you have correctly identified the dimensions, calculate the total surface area of the pyramid.

Interactive popup. Assistance may be required.

Check Your Answer

832 square feetClose Pop Up

Practice

  1. A box in the shape of a square pyramid is used to wrap packages of candies.

    2. Pyramid with dimensions labeled

    What is the total surface area of the box?

    Interactive popup. Assistance may be required.

    Hint

    SA = 1 over 2 1 2 Pl + BClose Pop Up Interactive popup. Assistance may be required.

    Check Your Answer

    1 over 2 1 2 (5 + 5 + 5 + 5)(4.5) + (5)(5) = 70 square inches Close Pop Up
  2. A decoration for a parade float will be in the shape of a rectangular pyramid. The people who designed the float have decided to paint the exposed faces of the pyramid, which will be resting on its base in the trailer used for the float.

Pyramid with dimensions labeled

What will be the total area that is painted?

Interactive exercise. Assistance may be required. Use the grid below to record your answer. Type your answer in the boxes in front of and behind the decimal. Click inside each box to enter the numeral that belongs in the box, and then click the bubble beneath the numeral to shade the bubble that matches the numeral. Incorrect portions of your answer will be shaded gray.

Interactive popup. Assistance may be required.

Hint

The only faces that will be painted are the lateral faces, which are triangles. Determine the sum of the areas of the 4 lateral faces.Close Pop Up

Click "Show Answer" to confirm that your gridded response is correct.