AMC 8 Daily Practice - Perimeter Tricks
Complete problem set with solutions and individual problem pages
The following figure is a side view of a staircase. It is known that each step is wide and high. What is the perimeter of the side of this staircase in meters?
- A.
- B.
- C.
- D.
- E.
Through translation, it can be known that the length of the staircase in the figure is , and the height of the staircase is .
Therefore, the perimeter of the side of the staircase is .
Note the unit conversion: .
Thus, the final answer is .
Seven identical rectangles, each with a length of and a width of , are arranged as shown in the figure below. What is the perimeter of this figure in centimeters?
- A.
- B.
- C.
- D.
- E.
As shown in the figure, the perimeter of the combined figure can be calculated using the formula: .
Given that the length and width , the perimeter of one rectangle is .
Substituting these values into the formula: .
Thus, the perimeter of the figure is .
What is the perimeter of the following figure?
- A.
- B.
- C.
- D.
- E.
Starting from point and walking clockwise around the figure, we mark the direction of movement and find that:
The sum of upward paths = the sum of downward paths =
The sum of rightward paths = the sum of leftward paths =
Therefore, the perimeter of the figure is: .
Thus, the final answer is .
A rectangle is divided into four pieces. Given that the perimeter of piece is , the perimeter of piece is , and the perimeter of piece is , what is the perimeter of the large rectangle?
- A.
- B.
- C.
- D.
- E.
Using the translation method, we know that:
The perimeter of the large rectangle = the perimeter of piece the perimeter of piece , which is .
Final answer: .
In the backyard, there is a rectangular flower bed with a square vegetable garden inside it. Emily wants to put a fence around its outer edge. What is the perimeter of the flower bed in feet?
- A.
- B.
- C.
- D.
- E.
The perimeter of the rectangle = .
Since , , and , , , we can calculate the perimeter of the rectangle as follows:
The perimeter of the rectangle
So the perimeter of the rectangular flower bed is feet.
In the diagram, all angles are right angles and the lengths of the sides are given in centimeters.Note the diagram is not drawn to scale. What is the length in , in centimeters?
- A.
- B.
- C.
- D.
- E.
Using the translation method, we find that:
Solving for :
Thus, the length of is .
A puppy starts at point , walks along the direction of , turns midway to walk parallel to , then turns again to walk parallel to , and continues this pattern until reaching point , then returns to along . Given that the perimeter of triangle is meters, how many meters does the puppy walk in total?
- A.
- B.
- C.
- D.
- E.
Using the translation method, we observe that the distance the puppy walks is exactly the perimeter of triangle .
Therefore, the total distance the puppy walks is:
A figure is formed by arranging small pieces of paper of the same size as shown in the diagram. Given that the length of each small piece of paper is centimeters, what is the total perimeter of the shaded parts in the figure?
- A.
- B.
- C.
- D.
- E.
As shown in the diagram, we can observe that lengths lengths widths.
Therefore, lengths widths.
Given that the length is , the width can be calculated as follows: .
The perimeter of one shaded part is .
Thus, the total perimeter of the shaded parts is: .
- 1
- 2
- 3
- 4
- 5
- 6
- 7
- 8
