Vocabulary
What is a composite figure?
A shape made up of two or more basic shapes.
What is the formula for the area of a rectangle?
A = length × width or A = l × w
A rectangle is 5 m long and 3 m wide. What is its area?
15 m²
Beth used the full circle formula for a semicircle. What should she have done instead?
Multiply the circle formula by ½.
Janie and Miguel need to paint around a circular logo on a rectangular wall. How do they find how much wall to paint?
Find area of wall (rectangle), then subtract area of logo (circle).
What does it mean to decompose a shape?
To break a complex shape into simpler ones to make calculations easier.
What is the formula for the area of a triangle?
A = ½ × base × height
A triangle has a base of 8 ft and a height of 6 ft. What is its area?
24 ft²
Jena used the diameter instead of the radius. Why is that wrong?
The formula uses radius, not diameter; using the wrong value overestimates the area.
A patio is 14 ft × 8 ft, and there's a 3 ft wide garden on each side. How much area is landscaped?
Total outer rectangle: (14+6)×(8+6) = 20×14 = 280 ft². Subtract patio: 112 ft². Landscaping = 168 ft².
What operation do you use to combine the areas of shapes in a composite figure?
Addition.
What is the formula for the area of a circle?
A = π × r²
Decompose a figure made of a rectangle and a triangle. How do you solve for area?
Find the area of each part using the correct formula, then add them together.
A student added the areas of overlapping shapes. What's the mistake?
They double-counted the shared area. Overlapping parts should only be counted once.
A mural has a triangle above a rectangle. How do you find the total area to paint?
Find area of triangle + rectangle, then add the two together.
What are two operations you might use when finding the area of composite figures?
Addition and subtraction.
What is the formula for the area of a trapezoid?
A = ½ × (base₁ + base₂) × height
A shape is made of a rectangle (10 × 4 m) and a triangle (base 10, height 4). Find total area.
Triangle: ½(10)(4) = 20 m²; Rectangle: 10×4 = 40 m²; Total = 60 m²
Someone used 3 for π instead of 3.14. How does that affect the result?
The answer is less accurate; it underestimates the area.
The shaded region is everything except a circle. What operation helps find that?
Subtraction: total area – area of circle.
Give an example of when you might subtract areas instead of adding them.
When there is a hole or cut-out in the figure, like subtracting a circular logo from a wall.
How do you find the area of a semicircle?
A = ½ × π × r²
A figure has a rectangle and a semicircle (radius 8). What’s the total area? (Use π = 3.14)
Rectangle not specified; semicircle = ½ × 3.14 × 8² = 100.48 units²
Explain and correct this mistake: ½(16)(12) + 3.14(16²).
They used the full circle area instead of half and used diameter instead of radius. Correct: ½(16)(12) + ½(3.14)(8²) = 96 + 100.48 = 196.48 units².
A figure has a trapezoid and a rectangle. The trapezoid's bases are 10 ft and 6 ft, height 4 ft. The rectangle is 10 ft by 3 ft. What's the total area?
Trapezoid: ½(10+6)(4) = 32 ft². Rectangle: 10×3 = 30 ft². Total = 62 ft².