Question

in november 1958 the cover scientific american showed this diagram on its cover. Each of the interior rectangles is a square. if square D is 81 spuare units and square c is 64 square units what is the area of the other seven squares? what is the area of the of the entire figure? what is the perimeter of the figure

Answer 1

From the 32 by 33 rectangular figure, having interior squares, we have

The area of the squares in square units are;

1. A = 324
2. B = 225
3. E = 100
4. F = 196
5. G = 16
6. H = 49
7. I = 1

• Area of the entire figure = 1056

• The perimeter of the figure = 130 units

How can the area and perimeter be found?

The areas in square units are;

Area of square A = 18 × 18 = 324

Area of square B = 15 × 15 = 225

Area of square E = 10 × 10 = 100

Area of square F = 14 × 14 = 196

Area of square G = 4 × 4 = 16

Area of square H = 7 × 7 = 49

Area of square I = 1 × 1 = 1

Area of a rectangle = Length × Breadth

Therefore;

Area of the entire figure = 32 × 33 = 1056

• Area of the entire figure = 1056 square units

The perimeter, P, of the rectangular figure is therefore;

P = 2 × 32 + 2 × 33 = 130

• The perimeter of the figure = 130 units

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