Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

# What is the area of these "L shapes"? Relevance

1.

A = LW - lw = (10)(8) - (5)(4) = 60 cm^2

2.

A = LW - lw = (12)(16) - (8)(9) = 120 cm^2  Answer//

• First picture

= red_area + blue_area → where: red_area = 6 * 8 = 48 cm²

= 48 + blue_area → where: blue_area = (10 - 6) * 3 = 4 * 3 = 12 cm²

= 48 + 12

= 60 cm²

Second picture

= red_area + blue_area → where: red_area = 7 * 12 = 84 cm²

= 84 + blue_area → where: blue_area = (12 - 8) * 9 = 4 * 9 = 36 cm²

= 84 + 36

= 120 cm² • Area, A1, of left...L-shape = [8*6+3(10-6)]cm^2 = 60cm^2.;

Area, A2, of right L-shape = [9(12-8)+7*12]cm^2 = 4(9+21)cm^2 = 120cm^2.

• See below for work and solutions. • Area = 60 cm^2

Area = 120 cm^2

• You can either cut them into smaller rectangles and add the results together or find the area of the large rectangle and subtract out the area of the void.  Either should give you the same results.

Looking at the first one.  With a base of 10 cm and 6 cm on the top, the length of the void is 4 cm.

The left has a length of 8 cm and right has a length of 3 cm so the void's length is 5 cm.

The area of the full rectangle is:

10 * 8 = 80 cm²

The area of the void is:

4 * 5 = 20 cm²

The difference is:

80 - 20 = 60 cm²

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If we add two smaller rectangles, cutting the shape into a large rectangle that is 8 x 6 and a smaller that is 4 x 3, we get:

8 * 6 + 4 * 3

48 + 12

60 cm²

We get the same result.

Now you choose one and do the same to the other shape.

• Area = length * width

8 * 10 - (8 - 3)*(10-6) = 8*10 - 5*4 = 80 - 20 = 60