Area, Perimeter, and Circumference Word Problems

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

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

In Hobbiton, hobbit houses have circular windows. A hobbit needs to replace a window which has a circumference of 4.8 metres. What is the area of the window?

Answer explanation

We need to find the radius first using the circumference formula: 

C = 2πr

4.8 = 2πr

4.8 = 2 × 3.14 × r

 r = 4.8 ÷ (2 × 3.14) 

 r = 0.764 metres

Calculate the area

A = πr²

A  = 3.14 × (0.764)²

       = 3.14 × 0.584 

The school is painting a mural on a wall shaped like a trapezium. The parallel sides of the wall are 8 metres and 12 metres long, and the height between them is 5 metres. How much paint will they need if 1L covers 10 square metres?

Answer explanation

Area of trapezium

= ½(a+b)h

= ½(8+12) × 5

= 50m²

Paint needed

= 50 ÷ 10

Hemi is creating a Maori-inspired artwork on a circular canvas. The outer edge of the canvas has a circumference of 188.4cm. He leaves a 5cm border around the edge unpainted. What is the area of the painted region?

Answer explanation

Radius of canvas

= Circumference ÷ (2π) = 188.4 ÷ (2π) = 30 cm

Area of canvas

= πr² = π × 30² ≈ 2827.43 cm²

Radius of painted area

= 30 - 5 = 25 cm

Area of painted region

= π × 25² ≈ 1963.5 cm²