Question

sam has proposed a design for his companys trucks. part a what is the sum of the perimeters, in units, of the five squares in the design? round your answer to the nearest tenth. enter your answer in the box. part b what is the sum of the areas, in square units, of the five squares in the design? round your answer to the nearest whole unit. enter your answer in the box.

Explanation:

Step1: Determine side - length of each square

Assume we can count the grid units for the side - length of each square from the graph. Let's say the side - lengths of the five squares are $a_1,a_2,a_3,a_4,a_5$.

Step2: Calculate perimeter of each square

The perimeter of a square is given by $P = 4s$, where $s$ is the side - length. So the perimeters are $P_1=4a_1$, $P_2 = 4a_2$, $P_3=4a_3$, $P_4=4a_4$, $P_5=4a_5$.

Step3: Calculate sum of perimeters

The sum of the perimeters $S_P=P_1 + P_2+P_3+P_4+P_5=4(a_1 + a_2+a_3+a_4+a_5)$.

Step4: Calculate area of each square

The area of a square is given by $A=s^2$. So the areas are $A_1=a_1^2$, $A_2=a_2^2$, $A_3=a_3^2$, $A_4=a_4^2$, $A_5=a_5^2$.

Step5: Calculate sum of areas

The sum of the areas $S_A=A_1 + A_2+A_3+A_4+A_5=a_1^2 + a_2^2+a_3^2+a_4^2+a_5^2$.

Since the graph is not provided with numerical values for side - lengths, we cannot give a numerical answer. But the general steps for Part A and Part B are as above. If we assume the side - lengths of the five squares are $s_1, s_2, s_3, s_4, s_5$ after counting from the grid:

Answer:

Part A: $4(s_1 + s_2 + s_3 + s_4 + s_5)$ (after substituting actual values and rounding to nearest tenth)
Part B: $s_1^2 + s_2^2 + s_3^2 + s_4^2 + s_5^2$ (after substituting actual values and rounding to nearest whole unit)