Question

Help solving this math

Answer 1

Answer:

1. 24 cm²
2. 6400 -1600π ≈ 1373.45 square units

Step-by-step explanation:

1. You can look at this several ways.

It can be considered to be a stack of 1+2+3 = 6 squares that are 2 cm on a side, so have a total area of 6 × (2 cm)² = 24 cm².

You can lop off one of the squares sticking out and put it into the empty corner to form a 6 cm by 4 cm rectangle with an area of (6 cm)(4 cm) = 24 cm².

You can consider it to be a 6 cm square with 3 squares cut out of it that are 2 cm on a side: (6 cm)² -3(2 cm)² = (36 -12) cm² = 24 cm².

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2. The shaded area is the difference in areas of a square 80 units on a side and a circle of 40 units radius. If we let d represent the side dimension of the square, then the area formulas are ...

  Square area = d²

  Circle area = π(d/2)²

So the difference area is ...

  shaded area = d² -(π/4)d² = d²(1 -π/4)

For d=80, the shaded area is ...

  shaded area = 80²(1 -π/4) = 6400 -1600π ≈ 1373.45 square units