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What is the best estimate of the area of the figure if each square has a side length of 1 mm?

27 square millimeters
36 square millimeters
39 square millimeters
46 square millimeters

What is the best estimate of the area of the figure if each square has a side length-example-1
User Exussum
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3.5k points

1 Answer

1 vote

Answer:

(c) 39 mm²

Explanation:

You want to know an estimate of the area of the irregular figure.

Decomposition

The areas of irregular figures are often easily computed by decomposing the figure into shapes whose areas have formulas. Here, we can draw a vertical line from the upper left vertex to divide the figure into a triangle on the left and a trapezoid on the right.

Triangle

The triangle has a base of 3 squares and a height of 6 squares, so an area of ...

A = 1/2bh = 1/2(3)(6) = 9 . . . . square mm

Trapezoid

The trapezoid has vertical parallel bases of 6 and 7 squares, and a width of 5 squares. Its area is ...

A = 1/2(b1 +b2)h = 1/2(6 +7)(5) = 65/2 = 32 1/2 . . . . square mm

Total area

Then the total area of the figure shown is ...

area = triangle area + trapezoid area

area = 9 mm² +32.5 mm² = 41.5 mm²

The closest estimate of those offered is 39 square mm.

User Benedict
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4.3k points