Perimeter of Polygons - SSAT Middle Level Quantitative

1. What is the perimeter of a rhombus with side length $s = 6$?

   $24$. All sides of a rhombus are equal, so multiply by 4.

2. What is the perimeter formula for a regular polygon with $n$ sides of length $s$?

   $P = ns$. Regular polygons have equal sides, so multiply the side length by the number of sides.

3. What is the perimeter of a regular octagon with side length $s = 2.5$?

   $20$. A regular octagon has eight equal sides, so multiply 8 by the side length.

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

   $18$. A regular hexagon has six equal sides, so multiply 6 by the side length.

5. Identify the perimeter of a parallelogram with side lengths $12$ and $5$.

   $34$. A parallelogram has two pairs of equal sides, so use $P = 2a + 2b$.

6. What is the perimeter of a triangle with side lengths $5$, $6$, and $8$?

   $19$. Sum the three given side lengths of the triangle.

7. What is the perimeter of a regular pentagon with side length $s = 4$?

   $20$. A regular pentagon has five equal sides, so multiply 5 by the side length.

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

   $P = a + b + c$. A triangle's perimeter is the sum of its three side lengths.

9. Find and correct the error: perimeter written as $2l + w$ for a rectangle with length $l$ and width $w$.

   Correct: $P = 2l + 2w$. The given formula omits one width; correct by including twice the width.

10. State the perimeter rule for composite shapes: how do shared edges affect the total perimeter?

    Add only outer edges; shared edges are not counted. Perimeter of composite shapes includes only external edges, excluding internal shared ones.

11. What is the missing side length $x$ if a triangle has perimeter $20$ and other sides $7$ and $5$?

    $x = 8$. Subtract the two known sides from the total perimeter to find the missing side.

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

    $P = 4s$. All four sides of a square are equal, so multiply the side length by 4.

13. What is the perimeter of two squares of side $5$ that share one full side?

    $30$. The composite forms a rectangle of dimensions $10 \times 5$, using $P = 2(l + w)$.

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

    $P = 2l + 2w$. Opposite sides in a rectangle are equal, requiring twice the length and twice the width.

15. State the formula for the perimeter of a polygon with side lengths $s_1, s_2, \dots, s_n$.

    $P = s_1 + s_2 + \cdots + s_n$. The perimeter of any polygon is the sum of the lengths of all its exterior sides.

16. What is the perimeter of a kite with adjacent sides $4, 4, 7, 7$?

    $22$. A kite has two pairs of adjacent equal sides, so sum all four lengths.

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

    $26$. Substitute the given length and width into the rectangle formula $P = 2l + 2w$.

18. What is the perimeter of a trapezoid with side lengths $3$, $5$, $6$, and $10$?

    $24$. A trapezoid's perimeter is the sum of its four side lengths.

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

    $28$. Apply the square formula $P = 4s$ with the given side length.

20. What is the missing side length $x$ if a rectangle has perimeter $P = 30$ and width $w = 6$?

    $x = 9$. Rearrange $P = 2x + 2w$ to solve for the missing length $x$.

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