Area Perimeter Circumference Word Problems

Ceyauna was helping Jada with a bulletin board. The bulletin board was 8 feet long and 6 feet wide. How many square feet of paper does Ceyauna need to cover the board?

• 14

• 28

• 48

Mrs. Apple just bought a new dinning room table. She needs to make a table cloth for decoration. What amount of fabric should she buy if the table has a diameter of 5 feet? Choose the equation that would best help solve this problem.

• C = π5

• C = (2)(π)(2.5)

• A = π5²

• A = π2.5²

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?

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

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?

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 

A school is renovating a classroom with an unusual shape. The room consists of a rectangle measuring 85m by 62m, with a semicircle attached to one of the longer sides. What is the total area of the floor that needs to be covered with new tiles?

Answer explanation

Area of rectangle

= 85 m × 62 m = 527 m²

Calculate the area of the semicircle:

 The diameter of the semicircle is equal to the length of the rectangle 

   - Radius of semicircle = 85 m ÷ 2 = 42.5 m

   - Area of full circle = πr² = π(42.5)² ≈ 567 m²

   - Area of semicircle = 567 m² ÷ 2 ≈ 284 m²

Total area = Area of rectangle + Area of semicircle

         = 527 m² + 284 m² 

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?