First Name: ____________________
Last Name:________________________________ Grade: _______
Teacher: ______________________ Parent’s email: ___________________________________________
Perimeter and Area
In this math challenge, we will be solving problems involving not only the perimeter of a two-dimensional object,
but also its area.
Kinder & First Grade: solve at least 3 problems.
Second & Third Grade: solve at least 6 problems.
Fourth Grade and above: solve at least 12 problems.
Problems
1.
Answer
What is the perimter of this shape?
25 [inches]
3 inches
4 inches
4 inches
3 inches
3 inches
8 inches
2.
What is the area of a piece of paper with a dimension of 4 inches by 5 inches?
20 [in²]
3.
The perimeter of the following rectangular garden is 18 feet. What is
the width of the garden?
Hint: a rectangle has 4 sides and two of its sides have the same length.
3 [feet]
6 feet
4.
Tim made a shape using 3 equilateral triangles as shown.
If each side of the triangle measures 3 inches, what is the perimeter of
the new shape?
15 [inches]
5.
Anil cuts a piece of wrapping paper that has a perimeter of 62 centimeters. If its length is
18 centimeters, what is its area?
234 [cm²]
6.
Find the area and the perimeter of the figure below.
Hint: there are multiple ways to solve this problem.
Area: 122
[cm²]
7 cm
10 cm
6 cm
Perimeter:
50 [cm]
15 cm
7.
How many square feet are there in 4 square yards? 1 yard = 3 feet, but 1 square yard ≠
3 𝑠𝑞 𝑓𝑒𝑒𝑡.
36 [ft²]
A square with an area of 1 square yard has sides that are 1 yard long. Since there are 3 feet in one yard, there
are 3 x 3 = 9 square feet in one square yard. Thus, there are 4 x 9 = 36 square feet in four square yards.
2016-2017 Math Challenge
8.
A
B
C
D
You can calculate the area of a triangle by multiplying the height and
the base of the triangle and divide the result by 2. For example, the
rectangle ABCD below measured 3 inches by 4 inches. The triangle
ABD can be calculated as (base x height) / 2 = (3 x 4) / 2 = 6 in².
Find the area of these two triangles:
a)
b)
8 yd
12 m
B
A
6 yd
18 m
9.
a. 108 [m²]
b. 24 [yd²]
A square and a rectangle have the same area. The rectangle has a length of 16 meters and
a perimeter of 50 m. What is the length of the square?
12 [m]
Width + Length of the rectangle = 50/2 = 25 m. Therefore, the width of the rectangle is 25-16 = 9 m.
Area of the rectangle: 9 x 16 = 144 m². Area of the square is also 144 m². Thus, the length of the square is 12 m.
10. How many 10-cm square floor tiles are needed to cover a floor that measures 5 meters by
8 meters? Note: 1 meter = 100 cm.
4000 [tiles]
500/10 = 50 squares
800/10 = 80 squares
Therefore, 50 x 80 = 4000 square tiles are needed to cover the floor.
11. The figure on the right is made up of 2 squares. The difference in their areas is 80
64 [cm]
cm². The perimeter is larger than 50 cm and if the sides of
both squares are whole numbers, what is the exact
measurement of the perimeter of the figure?
At first glance, there are two possible answers.
Two square numbers, which have a difference of 80 are 64 and 144, and 81 and
1. The perimeter of the figure then can be: 12+12+12+8+8+8+4= 64 cm or
9+9+9+1+1+1+8=38 cm. Since we are looking for a perimeter that is larger than 50cm, the answer is 64 cm
12. The figure below shows two overlapping squares.
What is the area of the unshaded region?
Area of the larger square: 8 x 8 = 64 cm²
Area of the small square: 6 x 6 = 36 cm²
Area of the shaded region: 5 x 4 = 20 cm²
Area of the unshaded region: 64 + 36 – 2 x 20 = 100 – 40 = 60 cm²
60 [cm²]
3 cm
8 cm
8 cm
2 cm
6 cm
6 cm
13. The figure below shows Mrs. Dorn’s rectangular garden. The garden is 21-meter-long and
15-meter-wide. Mrs. Dorn plans to lay square tiles
21 m
measuring 1.5 m by 1.5 m on the shaded path. How many
such tiles will she need?
18 m
12 m
15 m
44 [tiles]
Length: 21/1.5 = 14 tiles
Width: 12/1.5 =8 tiles. There are 14 tiles along the length and 8 tiles
along the width. Thus (14x8) x 2 = 44; Mrs. Dorn will need a total of 44
tiles.
2016-2017 Math Challenge
14.
The figure on the left is made up of 2 squares with side lengths of
24 inches and 16 inches. Find the area of the unshaded triangle.
The whole areas: 24 x 24 + 16 x 16 = 832 in²
Area of the shaded parts: ½ x (24+16) x 24 + ½ x 24x(24-16) + ½ 16x16 = 480 +
96+ 128 = 704 in². Area of unshaded triangle: 832 – 704 = 128 in²
15. Lucas has a rectangular sheet of construction paper that is 8 inches tall and has an area of
1 square foot. How many inches wide is Lucas’ sheet of paper?
The area of the sheet of paper is 1 square foot, which is equal to 12 x 12 = 144 square inches. Therefore, the
width of the paper is 144/8 = 18 inches.
2016-2017 Math Challenge