Perimeter From Diagrams - ISEE Lower Level Mathematics Achievement

1. What should you do if one exterior side length is not labeled but can be deduced?

   Use equal/opposite sides or subtraction to find it, then add. In symmetric or composite figures, deduce unlabeled outer sides using properties like congruence or by subtracting known lengths from totals.

2. What is the perimeter of a regular octagon with side length $s = 3$?

   $24$. Multiply the side length by eight, as a regular octagon has eight equal sides.

3. What is the perimeter of a square with side length $s = 7$?

   $28$. Apply the square perimeter formula $P = 4s$ by substituting $s = 7$.

4. What is the missing side length if a square has perimeter $P = 52$?

   $s = 13$. Solve for $s$ using the square formula rearranged as $s = \frac{P}{4}$.

5. What is the perimeter formula for a rectangle with length $l$ and width $w$?

   $P = 2l + 2w$. A rectangle has two pairs of equal sides, so the perimeter is twice the length plus twice the width.

6. What is the perimeter of a rectangle with $l = 10$ and $w = 2.5$?

   $25$. Use the rectangle perimeter formula $P = 2(l + w)$ with decimal width value.

7. What is the perimeter of a step-shaped figure with outer sides $8$, $3$, $2$, $2$, $6$, $5$?

   $26$. Add the lengths of all exterior sides in the step-shaped diagram for the total perimeter.

8. What is the perimeter formula for a triangle with side lengths $a$, $b$, and $c$?

   $P = a + b + c$. A triangle has three sides, so the perimeter is the sum of all three side lengths.

9. Identify the first step to find perimeter from a diagram with many sides.

   List all exterior sides and add their lengths. To calculate perimeter from a diagram, identify and sum only the lengths of the outer boundaries, excluding internal segments.

10. What is the perimeter in inches if a figure has outer sides $2$ ft, $3$ ft, $2$ ft, $3$ ft?

    $120$ in. Convert feet to inches ($1$ ft $= 12$ in) after summing sides, then multiply total feet by $12$.

11. What is the perimeter of a triangle if the diagram shows side lengths $x+2$, $x+3$, $2x$ and $x=4$?

    $21$. Substitute $x=4$ into each side expression and sum the resulting lengths.

12. What is the missing outer side if total perimeter is $40$ and the other outer sides sum to $27$?

    $13$. Subtract the sum of known outer sides from the total perimeter to find the missing length.

13. What is the perimeter in centimeters if a square has side length $0.4$ m?

    $160$ cm. Convert meters to centimeters ($1$ m $= 100$ cm), then apply the square perimeter formula.

14. What is the perimeter formula for a regular pentagon with side length $s$?

    $P = 5s$. A regular pentagon has five equal sides, so the perimeter is five times the side length.

15. What is the perimeter of a rectangle with $l = 9$ and $w = 4$?

    $26$. Apply the rectangle perimeter formula $P = 2(l + w)$ by substituting $l = 9$ and $w = 4$.

16. What is the perimeter of a triangle with side lengths $6$, $8$, and $10$?

    $24$. Sum the three given side lengths of the triangle as per its perimeter formula.

17. What is the perimeter of an L-shaped figure with outer sides $10$, $6$, $4$, $2$, $6$, $8$?

    $36$. Sum all listed outer side lengths of the L-shaped figure to obtain the perimeter.

18. What is the perimeter formula for a regular hexagon with side length $s$?

    $P = 6s$. A regular hexagon has six equal sides, so the perimeter is six times the side length.

19. What is the perimeter formula for a square with side length $s$?

    $P = 4s$. A square has four equal sides, so the perimeter is four times the side length.

20. What is the missing side length if a rectangle has $l = 12$ and perimeter $P = 34$?

    $w = 5$. Solve for $w$ using the rectangle formula rearranged as $w = \frac{P}{2} - l$.

21. What is the perimeter of a figure with outer side lengths $3$, $4$, $5$, and $6$?

    $18$. Add the lengths of all specified outer sides to find the total perimeter.

22. What is the perimeter of a regular hexagon with side length $s = 5$?

    $30$. Multiply the side length by six, as a regular hexagon has six equal sides.

23. What is the perimeter of a figure in a diagram?

    The total distance around the outside; sum of all outer side lengths. Perimeter measures the boundary of a shape by summing the lengths of all its exterior sides as shown in the diagram.

Study these flashcards