Relax – no one else knows the formula for that oddly shaped shaded region either! Shaded region questions nearly always involve subtraction. Usually, all you have to do is subtract the white area from the area of the whole figure are to get the gray.
Suppose you’re told that the length of a side of the larger square is 25, and the smaller square has sides of length 10. What is the area of the shaded region?
Simply use these 4 steps: English, Formulas, Substitute, Solve.
Step 1 (English) large square – small square = shaded region
Step 2 (Formulas) S2 – s2 = answer
Step 3 (Substitute) 252 – 102 = answer
Step 4 (Solve) 625 – 100 = 525
If you use these steps, most of these problems will be fairly easy. Need to subtract a semicircle? No problem; just use (πr2)/2.
Let’s do a trickier one:
Okay, the large and medium squares still have sides of 25 and 10, respectively. Suppose the small square has sides of length 3. What is the area of the unshaded region?
Step 1 (English) large square – medium square + small square = unshaded region
Step 2 (Formulas) l2 – m2 + s2 = answer
Step 3 (Substitute) 252 – 102 + 32 = answer
Step 4 (Solve) 625 – 100 + 9 = 534
If you didn’t see Step 1 right away, that’s okay. It’s easier if you break things down into simpler steps anyhow. Just find the area of the shaded region first (medium square – small square), and then subtract that from the large square (whole – gray = white).