some 1 centimeter squares are arranged in a staircase pattern. The drawing below shows a 3 step staircase. the area is 6 square centimeters and the perimeter is 12 centimeters.
what is the area and perimeter of a 10 step staircase?
pls help!
steps area perimeter
1 1 4
2 3 8
3 6 12
4 10 16
...
n n(n+1)/2 4n
so, 10 steps will have area 55 and perimeter 40
thank u so much steve!!
To find the area and perimeter of a 10-step staircase similar to the one described, we can use the information given about the 3-step staircase as a starting point.
Let's analyze the given 3-step staircase first. The drawing shows that the staircase has 3 rows, with each row containing a total of 3 squares. Since each square has dimensions of 1 centimeter by 1 centimeter, the total area of the 3-step staircase is 6 square centimeters (3 rows x 3 squares = 9 squares).
Now, let's find the perimeter of the 3-step staircase. The perimeter is the total length of the outer boundary of an object. In this case, since each square has sides measuring 1 centimeter, the perimeter of each row would be (1 + 1 + 1) centimeters = 3 centimeters. Since there are 3 rows, the total perimeter of the 3-step staircase is 3 centimeters x 3 rows = 9 centimeters.
Now, we can use the information we obtained from the 3-step staircase to find the area and perimeter of the 10-step staircase.
Area of the 10-step staircase:
Since the area of the 3-step staircase is 6 square centimeters and it consists of 9 squares, we can find the area of each square by dividing the total area of the 3-step staircase by the number of squares: 6 square centimeters ÷ 9 squares = 0.67 square centimeters per square.
A 10-step staircase will have 10 rows, and if each row contains 10 squares, the total area would be: 0.67 square centimeters per square x 10 rows x 10 squares = 67 square centimeters.
Perimeter of the 10-step staircase:
Since the perimeter of the 3-step staircase is 9 centimeters and it consists of 3 rows, we can find the perimeter of each row by dividing the total perimeter of the 3-step staircase by the number of rows: 9 centimeters ÷ 3 rows = 3 centimeters per row.
A 10-step staircase will have 10 rows, so the total perimeter would be: 3 centimeters per row x 10 rows = 30 centimeters.
Therefore, the area of the 10-step staircase is 67 square centimeters, and the perimeter is 30 centimeters.