Question

What is the perimeter of the figure in the diagram (round to three decimal places)? A) 44.471 B) 35.046 C) 32.471 D) 23.046

Answer 1

Answer:

The perimeter of the figure in the diagram is:

• D) 23.046

Step-by-step explanation:

To identify the perimeter of the figure shown, you must divide the figure in figures known, in this case, the top is a half of a circle, next is a rectangle, and the last could be divided into two triangles (image attached), so, we can define the perimeter of each figure identified:

1. Circle.

The circle has a diameter of 6 feet (six squares in the paper), now, you must remember that:

• PI = perimeter / diameter = 3.1416 approximately

How we know the diameter and the value of the PI, we can clear the perimeter:

• Perimeter = PI * diameter
• Perimeter = PI * 6 feet
• Perimeter = 18.849 feet

Remember this is the perimeter of a complete circle, but how we have a half circle, we must divide the perimeter obtained into 2:

• First Perimeter (a half of a circle) = 18.849 feet / 2 = 9.425 feet

2. Rectangle.

This is the easiest perimeter you can find, just need to add the 3 feet from the left side and the 3 feet from the right side, so:

• Second Perimeter (of a part of a rectangle) = 3 feet + 3 feet = 6 feet

3. Triangles.

The smallest triangle (please see the image attached) has the measures: 1 foot and 2 feet, to identify the hypotenuse you only must apply the Pythagoras theorem what is:

• Opposite leg squared + leg adjacent squared = hypotenuse squared

or  

• a^2 + b^2 = h^2

But how we need just the hypotenuse, we obtain the square root of all:

• square root (a^2 + b^2) = hypotenuse

Then we replace:

• Third perimeter = square root (1^2 ft + 2^2 ft) = 2.236 feet

And the last, for the biggest triangle, you use the same formula with square root but with the legs 5 feet and 2 feet:

• square root (a^2 + b^2) = hypotenuse
• Fourth perimeter = square root (5^2 + 2^2) = 5.385 feet

Now, you must add all the perimeters found:

• Perimeter of the figure = 9.425 feet + 6 feet + 2.236 feet + 5.385 feet
• Perimeter of the figure = 23.046 feet