Composite Figures Area Mastery Challenge

Finding areas of combined shapes Year 7 Mathematics STAAR-style problem solving

What Are Composite Figures?

Figures made from two or more basic shapes Common shapes: rectangles, triangles, circles Real-world examples everywhere around us Key skill for standardized tests

Shape Detective Challenge

Look at the composite figure Identify each basic shape within it Count how many shapes you can find Prepare to calculate total area

The Addition Method

Break figure into separate shapes Find area of each shape individually Add all areas together Total Area = Shape 1 + Shape 2 + Shape 3...

The Subtraction Method

Start with a larger basic shape Subtract areas of shapes that are removed Useful for figures with holes or cutouts Total Area = Large Shape - Removed Shapes

Circle Parts: Semicircles and Quarter Circles

{"left":"Semicircle = Half a circle\nArea = (π × r²) ÷ 2","right":"Quarter circle = One-fourth of a circle\nArea = (π × r²) ÷ 4"}

Step-by-Step Solution Practice

Given: Rectangle 8×6 with semicircle (radius 3) Step 1: Find rectangle area Step 2: Find semicircle area Step 3: Add them together

Challenge Question

A park has a rectangular field (20m × 15m) Quarter circles at each corner (radius 4m) What is the area of the walkable space? Think: Addition or Subtraction method?

STAAR Test Strategy Guide

Mastery Check: Key Takeaways

Break complex figures into basic shapes Use addition for combined shapes Use subtraction for shapes with cutouts Remember circle formulas: π × r² ÷ 2 or ÷ 4 Show all work for full credit