Measurement in Real Life

Year 11 NCEA Level 1 Mathematics – AS91945 & AS91947

Name:

Date:

Pair / Group:

Pacific community garden and tapa cloth illustration

📐 Formula Reference Card

Use these formulas to help you. Always write the formula first in your working!

Perimeter of a rectangle: P = 2 × (l + w) | Area of a rectangle: A = l × w | Area of a triangle: A = ½ × b × h

Composite shape area: Split into rectangles and/or triangles, calculate each, then add together. | Capacity (rectangular prism): V = l × w × h Remember: 1 cm³ = 1 mL | 1000 mL = 1 L

🌿 Part 1: Perimeter & Area Problems

For each problem: state the formula → substitute values with units → show full working → convert units if needed → write a sentence explaining your answer.

Problem 1 – Community Garden Fencing (Easier)
The Ōtāhuhu Community Centre is building a rectangular garden bed that is 12 m long and 7 m wide. They need to put a fence around the outside edge and lay grass matting to cover the ground inside.

(a) How many metres of fencing are needed? (Find the perimeter.)

Formula: P = ___________________________

My answer in a sentence:

(b) What is the area of grass matting needed to cover the garden bed?

Formula: A = ___________________________

My answer in a sentence:

Problem 2 – Tapa Cloth Design (Medium)
A Pacific student is creating a tapa cloth panel made up of a rectangle joined to a triangle on one end. The rectangle is 80 cm long and 50 cm wide. The triangle sits on the 50 cm end and has a height of 30 cm.

Find the total area of the tapa cloth panel. (Hint: calculate each shape separately, then add.)

Formula for rectangle: A = ___________________________

Formula for triangle: A = ___________________________

My answer in a sentence:

Problem 3 – Marae Hall Floor (Medium–Hard)
A marae hall floor is an L-shaped composite area. It can be split into two rectangles:
• Rectangle A: 10 m × 6 m
• Rectangle B: 4 m × 3 m

(a) Find the total floor area in m².

Formulas & Working:

My answer in a sentence:

(b) The hall needs new floor tiles. Each tile covers 0.5 m². How many tiles are needed to cover the entire floor?

My answer in a sentence:

💧 Part 2: Capacity & Unit Conversion Problems

Problem 4 – Water Storage Container (Medium)
A Pacific family in South Auckland uses a rectangular water storage container. It measures 60 cm long, 40 cm wide, and 50 cm high.

(a) Calculate the volume of the container in cm³.

Formula: V = ___________________________

(b) Convert your answer to litres. (Hint: 1 cm³ = 1 mL, and 1000 mL = 1 L)

My answer in a sentence:

Problem 5 – Hangi Pot Capacity (Hard)
A rectangular hangi pot is 45 cm long, 35 cm wide, and 30 cm deep. The pot is only filled to ¾ of its height with water.

(a) What is the full capacity of the pot in litres?

Formula: V = ___________________________

(b) How many litres of water are actually in the pot when filled to ¾ capacity?

My answer in a sentence: