Perimeter of Polygons - SSAT Middle Level: Quantitative

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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