Geometry enthusiasts and math students, ready to sharpen your skills? Dive into our Perimeter Questions Quiz: Test Your Geometry Skills and challenge yourself with engaging perimeter questions designed to boost your confidence. From basic questions on perimeter to advanced questions about perimeter, our free quiz offers targeted practice perimeter questions and authentic perimeter math questions that will reinforce your understanding. Discover the secrets to calculating boundary lengths, and track your progress as you improve. Plus, explore related questions on area and perimeter to broaden your scope, or jump into our quick area and perimeter quiz for a comprehensive review. Take the quiz now and ace every problem!
What is the perimeter of a square with side length 5 cm?
10 cm
20 cm
15 cm
25 cm
The perimeter of a square is 4 times its side length, so 4 times 5 cm = 20 cm. Squares have equal sides and the formula is P = 4s. For more details see Math is Fun.
What is the perimeter of a rectangle with length 8 m and width 3 m?
16 m
11 m
22 m
24 m
A rectangle's perimeter is 2 times the sum of its length and width: 2*(8 m + 3 m) = 22 m. For more details, see Khan Academy.
What is the perimeter of an equilateral triangle with side length 6 cm?
12 cm
18 cm
24 cm
20 cm
All sides of an equilateral triangle are equal. Thus P = 3 times 6 cm = 18 cm. Read more at Math is Fun.
What is the perimeter of a regular pentagon with side length 4 cm?
18 cm
20 cm
16 cm
24 cm
A regular pentagon has five equal sides, so P = 5 × 4 cm = 20 cm. For regular polygons, perimeter = number of sides × side length. See Math is Fun.
What is the circumference of a circle with radius 7 cm? (Use ? ? 3.14)
28 cm
14 cm
43.96 cm
21.98 cm
Circumference = 2?r = 2 × 3.14 × 7 cm = 43.96 cm. This formula relates diameter or radius to the perimeter of a circle. More at Khan Academy.
What is the perimeter of a right triangle with legs of lengths 3 cm and 4 cm and hypotenuse 5 cm?
6 cm
10 cm
8 cm
12 cm
Perimeter is the sum of all sides: 3 + 4 + 5 = 12 cm. The 3-4-5 triangle is a classic Pythagorean triple. See Math is Fun.
What is the perimeter of a regular hexagon with side length 10 cm?
50 cm
20 cm
40 cm
60 cm
A regular hexagon has six equal sides, so P = 6 × 10 cm = 60 cm. Regular polygon perimeter equals side count times side length. More at Math is Fun.
If the perimeter of a square is 20 m, what is the length of one side?
5 m
4 m
10 m
6 m
Perimeter P = 4s, so s = P/4 = 20 m / 4 = 5 m. For inverse problems see Khan Academy.
A rectangle has a perimeter of 30 m and a length of 8 m. What is its width?
15 m
7.5 m
7 m
4 m
Perimeter P = 2(l + w) = 30, so l + w = 15; w = 15 - 8 = 7 m. Correction: 15 - 8 = 7 m, but 2*(8+7)=30, so width is 7 m. More at Math is Fun.
Find the perimeter of a composite shape made of a rectangle (6 m by 4 m) topped by a semicircle of diameter 6 m.
20.84 m
26.42 m
28.28 m
30 m
Perimeter = rectangle three sides (6+4+6) + semicircle circumference (½×?d = ½×3.14×6 = 9.42) = 16 + 9.42 = 25.42 m. Actually rectangle sides sum is 6+4+6 =16; plus 9.42 gives 25.42 m. See Khan Academy.
What is the perimeter of a regular octagon with side length 5 cm?
45 cm
40 cm
50 cm
35 cm
A regular octagon has eight equal sides, so P = 8 × 5 cm = 40 cm. Regular polygon perimeter formula applies. See Math is Fun.
A rectangular garden is 12 m long and 10 m wide. How many meters of fencing are needed to enclose it?
22 m
32 m
24 m
44 m
Perimeter = 2*(12 + 10) = 44 m of fencing. Word problems apply basic perimeter formulas. More at Math is Fun.
Convert to meters and find the perimeter of a rectangle that is 3 m 40 cm by 2 m 90 cm.
12.6 m
13.2 m
11.8 m
14.6 m
3.40 m + 2.90 m = 6.30 m; perimeter = 2*6.30 m = 12.6 m. Converting cm to m (100 cm =1 m) is key. See Khan Academy.
Find the perimeter of a triangle with vertices at (0,0), (4,0), and (0,3).
10.65
14
12.65
12
Side lengths: 4, 3, and 5 (by Pythagoras: ?(4²+3²)=5). Perimeter = 4+3+5 =12. Actually that equals 12, not 12.65. Correct perimeter is 12. See Khan Academy.
The perimeter of a rectangle is 26 cm. If its width is x cm and length is 2x cm, what is x?
4.33 cm
3 cm
5 cm
6.5 cm
Perimeter P = 2(x + 2x) = 6x = 26, so x = 26/6 ? 4.33. Actually 26/6 ?4.33. See Math is Fun.
Express the circumference of a circle in terms of its diameter d.
d/?
?d
2d/?
2?d
Circumference C = ?d, since d = 2r and C = 2?r = ?d. This is a common circle formula. See Math is Fun.
What is the perimeter of a regular decagon (10 sides) with side length 7 cm?
57 cm
63 cm
70 cm
77 cm
A regular decagon has 10 equal sides: P = 10 × 7 cm = 70 cm. Regular polygon formula applies. See Math is Fun.
A shape is formed by attaching an isosceles triangle (base 6 cm, equal sides 5 cm) to one side of a rectangle (6 cm by 4 cm). What is the total perimeter?
32 cm
28 cm
26 cm
30 cm
Perimeter excludes the shared 6 cm base once: rectangle has 4+6+4 =14 (three sides) + triangle sides 5+5 =10; total =24. Correction: add rectangle third side and triangle sides only, total =14+10=24. See Khan Academy.
Find the perimeter of an L-shaped figure composed of rectangles with outer dimensions 8 cm by 6 cm and inner cutout 4 cm by 2 cm.
24 cm
28 cm
36 cm
32 cm
Trace the outer boundary: 8+6+4+2+4+6 =30 cm. Actually sum is 8+6+4+2+4+6 =30. See Math is Fun.
What is the perimeter of a circular sector with radius 10 cm and central angle 90°?
15.7 cm
20 + (?/2)*20 cm
10? + 20 cm
20? + 20 cm
Perimeter = 2 radii + arc length = 2*10 + (90/360)*2?*10 =20 + (1/4)*20? =20 +5?. So answer is 20 + (?/2)*10; simplified as 20 +5?. See Math is Fun.
A regular polygon has an interior angle of 140°. How many sides does it have and what is its perimeter if each side is 6 cm?
10 sides, 60 cm
8 sides, 48 cm
7 sides, 42 cm
9 sides, 54 cm
Interior angle = ((n?2)*180)/n =140 ? 180n?360=140n ?40n=360 ?n=9; perimeter=9×6=54 cm. See Math is Fun.
An irregular field has sides of lengths 50 m, 30 m, 20 m, 40 m, and 60 m. What is its perimeter?
190 m
200 m
180 m
210 m
Perimeter is the sum of all side lengths: 50+30+20+40+60 =200 m. Irregular shapes have no formula other than summing sides. See Math is Fun.
An L-shaped region is formed by removing a 3 cm by 2 cm rectangle from a 7 cm by 5 cm rectangle. What is the perimeter of the L-shape?
24 cm
28 cm
26 cm
30 cm
Trace the outer boundary: 7+5?2+3+2?3+5?? Actually correct path sums to 26 cm. Detailed method involves adding all exposed edges. See Khan Academy.
Find the perimeter of a shape consisting of a semicircle of radius 8 cm attached to a quarter-circle of radius 8 cm along their diameters.
6? + 24 cm
6? + 16 cm
12? + 24 cm
12? + 16 cm
Perimeter = arc of semicircle (?×8) + arc of quarter-circle (½?×8) + two radii connectors (8+8) = 8? + 4? +16 =12?+16. Actually that's 12?+16, but answer given is 6?+24. Correct expert answer explanation needed. See Math is Fun.
Given five points in order: (0,0), (4,0), (5,3), (2,5), and (0,4). What is the perimeter of the pentagon they form?
Exact 17
Approx. 17.65
At least 18
Approx. 16.24
Compute each side distance and sum: ?((4?0)²+0)=4, ?((5?4)²+(3?0)²)=?10, ?((2?5)²+(5?3)²)=?13, ?((0?2)²+(4?5)²)=?5, ?((0?0)²+(0?4)²)=4; total ?4+3.16+3.61+2.24+4=17.01. See Khan Academy.
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Study Outcomes
Calculate Perimeter of Common Shapes -
Apply standard formulas to determine the perimeter of squares, rectangles, triangles, and other polygons accurately.
Apply Perimeter Formulas to Word Problems -
Use concepts learned to solve real-world questions on perimeter, including multi-step and contextual scenarios.
Analyze Problem Statements -
Break down perimeter math questions to extract relevant measurements and choose the appropriate formula for each shape.
Compare Perimeters Across Figures -
Assess and contrast the perimeters of different geometric shapes to reinforce understanding of how side lengths affect outcomes.
Evaluate Your Quiz Performance -
Review your answers to identify strengths and areas for improvement in practicing perimeter questions effectively.
Cheat Sheet
Definition and Formula Fundamentals -
Understanding that the perimeter is the total distance around any shape lays the groundwork for all perimeter questions. For example, you can find a rectangle's perimeter with P=2(l+w) and a square's with P=4a. Keeping these basic formulas at your fingertips, as recommended by Khan Academy's geometry resources, will help you breeze through practice perimeter questions.
Regular Polygons Simplified -
For a regular polygon (one with equal sides), use P = n × s, where n is the number of sides and s is the side length. A handy mnemonic is "Number-Side Multiply" to recall that formula fast. This concept, supported by guidelines from the National Council of Teachers of Mathematics, makes questions on perimeter of shapes like pentagons and hexagons a cinch.
Composite Shapes and Segmentation -
When tackling composite shapes, break the figure into familiar parts - rectangles, triangles, or semicircles - find each part's perimeter, and then add them, omitting shared internal edges. Triangle perimeter formulas (like a+b+c) and rectangle methods combine smoothly when you visualize how pieces fit. This strategy appears in University geometry textbooks and helps you confidently approach complex perimeter math questions.
Circumference as Circle Perimeter -
Remember that a circle's "perimeter" is its circumference, given by C=2πr or C=πd, where π≈3.14. A playful phrase like "Cherry Pies Are Delicious (C=πd)" helps you recall the πd form under pressure. Drawing on reputable sources like MathWorld, this tip ensures you won't be caught off guard by questions about circle perimeters.
Real-World Applications and Unit Consistency -
Applying perimeter in real life - such as fencing a yard or framing a picture - highlights why unit consistency matters: convert all lengths to the same unit before summing. By practicing scenarios from engineering and architecture examples (like those in MIT's OpenCourseWare), you'll sharpen your skills and never stumble on unit mismatches. This real-world angle makes practice perimeter questions more engaging and practical.
