Area, Perimeter, Circumference Word Problems

A plan for a new rectangular swimming pool has an area of 50 square meters and a perimeter of 30 meters. What are the length and width?

Two pizzerias are competing for business. Pizzeria A offers a square pizza with sides measuring 40cm, while Pizzeria B offers a circular pizza with a diameter of 45cm. Which pizzeria offers more pizza (in terms of area), and by how many square centimetres?

Answer explanation

Calculate the area of the square pizza (Pizzeria A)

- A = 40 cm × 40 cm = 1,600 cm²

Calculate the area of the circular pizza (Pizzeria B)

- Formula for area of a circle: A = πr²

 - radius = 45 cm ÷ 2 = 22.5 cm

- A = π × (22.5 cm)²

- A ≈ 3.14 × 506.25 cm² ≈ 1,589.63 cm²

Compare the areas

- Square pizza (Pizzeria A): 1,600 cm²

- Circular pizza (Pizzeria B): 1,589.63 cm²

- Difference = 1,600 cm² - 1,589.63 cm² = 10.37 cm²

Farmer John walks his pet pig around his barn every day. The barn is 25 meters by 12 meters. If we walks the pig around the barn three times, how many meters did farmer John and his pig walk?

Mia wants to build a fence around her rectangular garden. The garden measures 8.6 metres long and 6.1m wide. How much fencing material does she need to purchase?

Answer explanation

Perimeter = 2(length + width) = 2 × (8.6 + 6.1)

=  29.4 metres

Fencing Material = 30m

A kitchen floor is 35 m by 50 m. New tiles are needed for the floor. If one tile covers 25 square metres of space, how many tiles will be needed to cover the floor?

Jackson cut a regular pentagon out of poster board to make sign for his door. The perimeter of the sign is 34.8cm. What is the length of each side of the sign?

Alicia's garden is 50 square metres. Inside of her garden she plants a section of tomatoes that is 3m by 4m. How much more space does she have left in her garden to plant other crops? 

A triangular wall needs to be painted. The triangle is an equilateral triangle with 35 metre sides and the height of the wall is 30 metres. Nina wants to make a gold border around the wall. What is the length of the gold border that is needed?

Answer explanation

An equilateral triangle means that all 3 sides are equal. This means you need to add up all 3 sides to get the length of the gold border.

The garden has two sections: a triangle section for vegetables and a circular section for flowers, with the rest grass. The vegetables section is a right-angle with sides of 3.45m and 2.1m. The flower section is 5.7m from one side to the other. What is the total area of each section of the garden? If grass seed costs $1.77/m², how much will it cost to buy enough seed for the grass area?

Answer explanation

Vegetable Section (Triangle)

Area of triangle = (base × height) ÷ 2

Area = (3.45 × 2.1) ÷ 2 = 3.6225 m²

Flower Section (Circle)

Area of circle = π × r²

Where r is the radius (half the diameter) - Radius = 5.7 ÷ 2 = 2.85m

Area = π × 2.85² ≈ 25.5173 m²

Grass Section

subtract vegetable and flower areas from the total garden area.

TOTAL GARDEN AREA: 52.46m² (8.6 x 6.1)

VEGETABLE & FLOWER GARDENS:

3.6225 m² + 25.5173 m² = 29.1398m²

GRASS AREA = 52.46 - 29.1398 = 23.32m²

Grass Seed Cost = Grass area × Price per m²

         = 23.32m² × $1.77/m²  = 41.2764

         = $41.30

For a school event, circular pizzas with a radius of 12cm are ordered. If each student should get 50cm² of pizza, how many students can one pizza feed?

Answer explanation

Area of pizza = πr² = π × 12² =  452.39 cm²

Number of students = 452.39  ÷ 50 ≈ 9.05

= 9 students