Properties of Rectangles

Show your work for each problem.

1.
How many right angles does a rectangle have?
1. a)6
2. b)4
3. c)3
4. d)2
Answer: 2
A rectangle has exactly 4 right angles (90°). This is one of its defining properties.
2.
Which property is TRUE about the diagonals of a rectangle?
1. a)They are perpendicular
2. b)They do not intersect
3. c)One is longer than the other
4. d)They are congruent (equal length)
Answer: They are congruent (equal length)
The diagonals of a rectangle are congruent, meaning they have equal length. They also bisect each other, but they are NOT perpendicular (that's a property of squares and rhombuses).
3.
A rectangle has a length of cm and a width of cm. What is its perimeter in cm?
Answer: 32
cm
4.
A rectangle has a length of m and a width of m. What is its area in m²?
Answer: 40
m²
5.
Is a square a rectangle?
1. a)No, never
2. b)Only if it's large
3. c)Only sometimes
4. d)Yes, always
Answer: Yes, always
Yes! A square has 4 right angles and opposite sides that are equal, so it meets all the requirements of a rectangle. A square is a special type of rectangle where all 4 sides are also equal.
6.
A rectangle has sides of cm and cm. What is the length of its diagonal in cm?
Answer: 5
cm. This is a 3-4-5 right triangle!
7.
A rectangular garden is m long and m wide. Calculate its perimeter.
Answer: 42
1. What is the perimeter formula for a rectangle? 2(l + w)
2. What is ? 21
3. What is ? 42
8.
Find the diagonal of a rectangle with length cm and width cm.
Answer: 13
1. What is ? 25
2. What is ? 144
3. What is ? 169
4. What is ? 13
9.
In rectangle ABCD, the diagonals intersect at point E. If diagonal AC = cm, what is the length of AE?
1. a)14 cm
2. b)3.5 cm
3. c)28 cm
4. d)7 cm
Answer: 7 cm
Since diagonals bisect each other, E is the midpoint of AC. Therefore, cm.
10.
A rectangular room is m long and m wide. How many square meters of carpet are needed to cover the floor?
Answer: 28
Area m². You need 28 square meters of carpet.
11.
A rectangle has a perimeter of cm and a length of cm. Find its width.
Answer: 6
1. Use P = 2(l + w). What is (l + w) if P = 30? 15
2. If l + w = 15 and l = 9, what is w? 6
12.
A rectangle has an area of cm² and a width of cm. Find its diagonal length.
Answer: 10
1. If Area = l × w and Area = 48, w = 6, what is l? 8
2. What is ? 36
3. What is ? 64
4. What is ? 100
5. What is ? 10
13.
A rectangle has diagonals that are each cm long. If the width is cm, what is the length in cm?
Answer: 8
. Therefore cm.
14.
If you double both the length and width of a rectangle, how does the diagonal change?
1. a)It stays the same
2. b)It halves
3. c)It quadruples
4. d)It doubles
Answer: It doubles
New diagonal = . The diagonal doubles!
15.
A TV screen is cm wide and cm tall. What is the screen size (diagonal) in cm?
Answer: 100
1. What is ? 6400
2. What is ? 3600
3. What is ? 10000
4. What is ? 100