Question

Identify the area of the figure rounded to the nearest tenth

Answer 1

118.7 inches squared.

Explanation:

What is the area?

The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

What is diameter?

Diameter is the length across the entire circle, the line splitting the circle into two identical semicircles.

The expression for solving the area of a circle is A = π ×
`r^(2)`.

To solve for the semicircle above, we can divide the diameter into 2 to get the radius.

• 12 ÷ 2 = 6

So, the radius of the upper semicircle is 6 inches.

If the radius of a circle is 6 inches, then you can substitute r for 6 into the formula.

• A = π ×
  `6^(2)`

This simplifies to A = 36π. If a semicircle if half the size of a normal circle, then it will be A = 18π, because 36 ÷ 2 = 18.

To solve for the lower semicircle, we can do the same this as we did above.

• A = π ×
  `r^(2)`

But wait, we don't know the radius or diameter!

No worries! To solve for the diameter of the circle, we can take the line that is parallel to the semicircle (the one that has a length of 12in) and subtract 6 from it. We subtract 6 from it because the semicircle takes up the remaining length of the line, not including the 6in.

To solve for the lower semicircle, we can divide the diameter by 2 to get the radius.

• 6 ÷ 2 = 3

So, the radius of the circle is 3.

Now we can insert 3 into the expression.

• A = π ×
  `3^(2)`

This simplifies to A = 9π. If a semicircle if half the size of a normal circle, then it will be A = 4.5π because like above, 9 ÷ 2 = 4.5.

Adding the two semicircles together:

• 18π + 4.5π = 22.5π

• 22.5 × π ≈ 70.6858

So, the area of both semicircles is approximately 70.6858 square inches.

To solve for the area of a rectangle we use the expression:

• A = length × width

Inserting the dimensions of the rectangle:

• 8 × 6 = 48

So, the area of the rectangle is 48 square inches.

Adding the two areas together:

• 70.6858 + 48 = 118.6858 ≈ 118.7

Therefore, the area of the entire figure, rounded to the nearest tenth is
`118.7`
`in^(2)`.