Mathematics • Year 8 • Unit 3 • Lesson 5
Area of Rectangles and Triangles
Build fluency with A = lw for rectangles and A = ½bh for triangles. One worked rectangle example, one guided triangle example with blanks, then eight problems on rectangles, triangles, finding sides, and a composite.
1. I do, fully worked example
Two essentials: A = l × w for rectangles, and units MUST be squared (cm², m²) because area is 2D.
Problem. A rectangular deck is 12.5 m long and 4.8 m wide. Find its area.
Step 1, Identify the shape and dimensions.
Rectangle: l = 12.5 m, w = 4.8 m.
Reason: rectangles need length AND width. Both are already in the same units (m).
Step 2, Write the formula.
A = l × w
Reason: rectangle area = length × width. Always write the formula before substituting.
Step 3, Substitute and calculate.
A = 12.5 × 4.8 = 60
Reason: 12.5 × 4.8 = 12.5 × 4 + 12.5 × 0.8 = 50 + 10 = 60. Or use long multiplication.
Step 4, Add squared units.
A = 60 m²
Reason: m × m = m². Area is ALWAYS in squared units, never plain m or cm.
Answer: A = 60 m².
2. We do, triangle with blanks
Triangles need the PERPENDICULAR height, the height at right angles to the base. Don't use the slant side! 4 marks
Problem. A triangle has a base of 10 cm and a perpendicular height of 7 cm. Find its area.
Step 1, Identify base and height:
b = ______ cm, h = ______ cm (h is ______ to b, at 90°)
Step 2, Write the formula:
A = ½ × ______ × ______
Step 3, Substitute and calculate:
A = ½ × 10 × 7 = ½ × ______ = ______
Step 4, Add squared units:
A = ______ cm²
3. You do, independent practice
Show all working. The first four are foundation (direct application). The middle two are standard (find a missing side). The last two are extension (right triangles and a composite).
Foundation, calculate directly
3.1 A rectangle is 9 cm × 5 cm. Find A. 1 mark
3.2 A square has side length 8 m. Find A. (Hint: A = s².) 1 mark
3.3 A triangle has b = 12 cm and perpendicular h = 5 cm. Find A. 1 mark
3.4 A triangle has b = 14 m and perpendicular h = 9 m. Find A. 1 mark
Standard, find a missing side
3.5 A rectangle has A = 72 cm² and length 9 cm. Find the width. 2 marks
3.6 A triangle has A = 30 cm² and base 12 cm. Find the perpendicular height. (Hint: 30 = ½ × 12 × h, so h = 30 × 2 ÷ 12.) 2 marks
Extension, right triangles and composites
3.7 A right-angled triangle has legs of 10 cm and 7 cm. Find its area. (Hint: in a right triangle, the two legs are automatically perpendicular, use them as base and height.) 2 marks
3.8 An L-shaped room is formed from a 10 cm × 8 cm rectangle with a 4 cm × 3 cm corner removed. Find the area. (Hint: total area − removed area.) 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2, We do (triangle b = 10, h = 7)
Step 1: b = 10 cm, h = 7 cm (h is perpendicular to b).
Step 2: A = ½ × 10 × 7.
Step 3: A = ½ × 70 = 35.
Step 4: A = 35 cm².
3.1, Rectangle 9 × 5
A = 9 × 5 = 45 cm².
3.2, Square s = 8
A = s² = 8² = 64 m².
3.3, Triangle b = 12, h = 5
A = ½ × 12 × 5 = ½ × 60 = 30 cm².
3.4, Triangle b = 14, h = 9
A = ½ × 14 × 9 = ½ × 126 = 63 m².
3.5, Rectangle A = 72, l = 9
w = A ÷ l = 72 ÷ 9 = 8 cm.
3.6, Triangle A = 30, b = 12
From A = ½bh: 30 = ½ × 12 × h = 6h, so h = 30 ÷ 6 = 5 cm.
3.7, Right triangle, legs 10 and 7
The legs are perpendicular, so use them as b and h directly: A = ½ × 10 × 7 = 35 cm².
3.8, L-shape 10 × 8 with 4 × 3 cut
Total = 10 × 8 = 80 cm². Cut = 4 × 3 = 12 cm². L-shape A = 80 − 12 = 68 cm².