SAT Math: Find the area of composite (combined) shapes
18+ practice questions in Praczo
The concept, explained
- 1
Break the shape into non-overlapping basic shapes (rectangles, triangles, circles, semicircles) whose areas you already know.
- 2
Add the areas when the pieces combine to form the whole shape. Subtract when a region is cut out (e.g., a circle removed from a square).
- 3
Label every dimension before computing. Many composite problems hide dimensions — use total lengths minus known pieces to fill them in.
- 4
For shapes with a semicircle, treat the semicircle’s diameter as one side of the attached rectangle. Its area is (1/2)πr².
- 5
Keep π symbolic until the end — simplify once, not at every step, to avoid rounding errors.
- ✗ Using the wrong radius for a circular piece — remember that radius is half the diameter, not the diameter itself.
- ✗ Forgetting to subtract cut-out regions, leading to an overestimate of the area.
- ✗ Applying a triangle or rectangle formula to the wrong base/height pair after cutting the shape.
SAT-style practice
A figure is formed by a rectangle of width 8 and height 6 with a semicircle attached to the right side of the rectangle (diameter equal to the height). What is the total area of the figure?
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