Area and Perimeter — Polygons and Circles

SAT Math · Axiom Academy

Area & Perimeter of Polygons & Circles Master the formulas for calculating areas and perimeters of rectangles, triangles, circles, and composite shapes. In this lesson, you'll master: Area and perimeter formulas for common polygons (rectangles, triangles, parallelograms) Circumference and area formulas for circles How to find areas of composite shapes by breaking them into simpler pieces Real SAT-style multi-step problems involving area and perimeter A rectangle has four right angles and opposite sides are equal. A rectangle has length 12 cm and width 5 cm. What is its area? We need the area of the rectangle. A parallelogram has two pairs of parallel sides. The area depends on the base and height, not the slant sides. A triangle has a base of 10 inches and a height of 6 inches. What is its area? Base = 10 inches, Height = 6 inches A circle has a radius of 4 cm. Find its circumference and area. Answers: Circumference = cm (≈ 25.1 cm), Area = square cm (≈ 50.3 square cm) Composite Shapes & Shaded Regions Many SAT questions ask for the area of composite shapes or shaded regions. The key strategy is to break the shape into simpler pieces . Strategy: "Big Shape Minus Small Shape" Identify the big shape (outer boundary) Identify the small shape(s) to subtract (unshaded area) Calculate: Shaded Area = Area(Big) − Area(Small) A square with side length 10 cm has a circle with radius 3 cm removed from its center. What is the area of the shaded region (the square minus the circle)?

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