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# Tip #20 to Get a Top ACT Math Score (page 2)

By McGraw-Hill Professional
Updated on Sep 7, 2011

1. D When a picture is described and not shown, draw it. That helps you see what to do next, and it helps avoid careless error. The area of the remaining portion equals the area of the wall minus the area of the windows:
2. Area wall – 3(area window) = area remaining portion

(7)(10) – 3(2)(2) = area remaining portion

70 – 12 = area remaining portion

58 = area remaining portion

3. K The word "circumscribed" throws some kids. But, in this book you'll learn all that you need for the ACT. When they throw a tough word at you that we have not discussed in this book, they'll define it in the question or you won't even need it. Here we don't need the word; you can cross it out. It's totally implicit in the diagram. "Circumscribed" just means "drawn around." So the square is drawn around the circle, which is obvious from the diagram anyway! So don't get intimidated. Stay confident and focused. So, the area around the circle equals the area of the square minus the area of the circle. "Mmmm … donuts!"
4. Area square – area circle = area around circle (18)(18) – π(9)2 = 324 – 81(π)

5. C Some kids see this and say, "I don't know the formula for the area of a trapezoid, so I can't do it." It's true that you could solve this question with the trapezoid formula, but you can also use donuts. They give you a back door on purpose. Don't get intimidated. Stay with it and look for another way! The area of the shaded trapezoid equals the area of the rectangle minus the areas of the two triangles:
6. Area trapezoid = area rectangle – area of triangles

Area trapezoid = 48 – 0.5(6)(4) – 0.5(3)(4)

Area trapezoid = 48 – 12 – 6 = 30

7. H First, always label all the info from the question into the diagram. That helps you see what to do next and to avoid careless errors. The area of the shaded region equals the area of the big square minus the area of the small square. We can do that with some special right triangles or Pythagorean theorems (Skills 25 and 24), but we can also just calculate the area of a shaded triangle and multiply by 4.
8. Area shaded = 4(area triangle)

Go to: Tip #21