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Area review Area is the space inside a 2-D shape. Area is always in square units (for example, in2, ft2, yds2, cm2, m2). Think of covering a shape with a bunch of square area rugs. Be careful not to confuse area with perimeter! Story problem strategy: Draw a diagram of the situation. Finding area Rectangle w (working “forwards”) Given area, finding a side length [harder] Multiply length by width. (working “backwards”) Divide area by the width to find the length. A = Lw L= L Parallelogram Multiply base by height. h h= NOTE: Height is always at a right angle with the base. It’s never the slanting side. A = s2 s HINT: You use squaring for squares, not for rectangles or parallelograms. 𝐿 𝐴 𝑏 Divide area by the height to find the base. b= Square the side length. 𝐴 Divide area by the base to find the height. A = bh Square 𝑤 Divide area by the length to find the width. w= b 𝐴 𝐴 ℎ Take the square root of the area to find the side length. s = √𝐴 HINT: You use square roots for squares, not for rectangles or parallelograms. D. Stark 4/2/2016 Finding area Multiply base by height and then find half of that (either multiply by ½ or divide by 2). A triangle is half a parallelogram. Triangle h b A = ½ bh or h A= b h b EXAMPLE (requires algebra): If the area of a triangle is 60 m2, and the base is 20, what’s the height? A = ½ bh 60 = ½ (20)h 60 = 10h 𝑏ℎ 60 2 10 NOTE: Height is always at a right angle with the base. It’s never the slanting side. = 10ℎ 10 h=6m Find the average of the two bases. Then multiply by height. Trapezoid b2 h b1 Given area, finding a side length [harder] A = ½ (b1 + b2)h NOTE: Height is always at a right angle with the base. It’s never the slanting side. NOTE: It doesn’t matter which you call b1 and which b2. Circle r Multiply by the radius squared. Use 3.14 as an approximation for . A = r2 d NOTE: Don’t confuse area with circumference (C= 2r or C= d EXAMPLE (requires algebra): If the area of a circle is 78.5 m2, what’s the radius? A = r2 78.5 3.14r2 78.5 3.14 25 = r2 r=5m 3.14𝛤2 3.14 [To find r, take the square root.] D. Stark 4/2/2016