If six people share the whole cake, then three people will share half the cake. One way to divide the cake in half is shown here.
Each half of the cake is 18 inches on its two outer edges. So each person should receive 18/3, or 6 inches, of the cake’s outer edge.
To check the areas of the three pieces, use the formula for the area of a triangle:
Area = (1/2) base × height
The height of triangles 1 and 3 in the diagram is half the width of the cake, or 4.5 inches. Since the length of each base is 6 inches, the area of each of these two triangles is:
A = (1/2) × 6 × 4.5 = 13.5 in2
The area of shape 2 is half the area of the entire cake, minus the area of triangles 1 and 3:
Area of half = (1/2) × 9 × 9 = 81/2 = 40.5, or 40.5 in2AreaTriangle1 = AreaTriangle3 = (1/2) × 6 × 4.5 = 13.5, or 13.5 in2AreaRegion2 is Area of half of the cake – AreaTriangle1 – AreaTriangle3AreaRegion2 = (1/2) × 9 × 9 –13.5 – 13.5 = 13.5, or 13.5 in2
Therefore, these three pieces represent equal shares. The other half of the cake can be divided similarly.
There are other ways to cut the cake into six equal shares. For example, you could start by dividing the cake into two rectangles of the same size and shape.