Surface Area Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
Find the surface area of a rectangular prism with length 44 cm, width 33 cm, and height 55 cm.

Solution

  1. 1
    A rectangular prism has 6 faces forming 3 pairs of identical rectangles. Label the pairs: l×wl \times w (top/bottom), l×hl \times h (front/back), w×hw \times h (left/right). Total: SA=2(lw+lh+wh)SA = 2(lw + lh + wh).
  2. 2
    Substitute l=4l = 4 cm, w=3w = 3 cm, h=5h = 5 cm: calculate each pair — lw=12lw = 12, lh=20lh = 20, wh=15wh = 15.
  3. 3
    Compute: SA=2(12+20+15)=2(47)=94SA = 2(12 + 20 + 15) = 2(47) = 94 cm². Each pair of faces contributes twice to the total surface.

Answer

SA=94 cm2SA = 94 \text{ cm}^2
Surface area is the total area of all faces of a 3D shape. For a rectangular prism, compute the area of each distinct face and double it (since opposite faces are congruent).

About Surface Area

The total area of all the faces or surfaces that enclose a three-dimensional object, measured in square units.

Learn more about Surface Area →

More Surface Area Examples

Example 2 medium

Find the surface area of a cylinder with radius [formula] cm and height [formula] cm. Leave your ans

Example 3 easy

Find the surface area of a cube with side length [formula] cm.

Example 4 medium

A cube has surface area [formula] cm². Find the length of one edge.

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