Ready Find the Area of Polygons – Quiz – Level F Richard makes a number 7 by cutting out a rectangle and a parallelogram. Find the area of the number 7. Are
The Correct Answer and Explanation is:
Area of the figure: 57 cm²
Break the blue “7” into the two shapes Richard cut: a rectangle for the top bar and a parallelogram for the slanted leg. Because the pieces merely touch, the digit’s area equals the sum of their areas.
1. Rectangle (top bar)
The bar is labelled 7 cm long and 3 cm tall. A rectangle’s area is
7 cm × 3 cm = 21 cm².
2. Parallelogram (leg)
Area of a parallelogram = base × height, with height measured perpendicular to the base. The entire left slanted edge is labelled 9 cm, so that edge is the base. A dashed segment drops to the opposite side, carries a right-angle symbol, and is labelled 4 cm, so it is the height. Thus
9 cm × 4 cm = 36 cm².
3. Combine
Add the non-overlapping parts: 21 cm² + 36 cm² = 57 cm².
4. Why the method works
The Addition Postulate for area states that when regions do not overlap, the total area is the sum of the parts. Choosing shapes whose side lengths are shown avoids any guesswork. The dashed altitude and right-angle mark guarantee that 4 cm is perpendicular to the 9 cm base, letting us multiply those values directly. Finally, rectangles and parallelograms share the same simple area rule (base times height), so the calculation is quick.
Common pitfalls to avoid
Many students mistakenly multiply the 9 cm by the 7 cm, thinking those are the two numbers that matter. That gives 63 cm², which is large, because the 7 cm side belongs to the rectangle, not the parallelogram. Others try to use the 9 cm as the height. The right-angle symbol shows that 9 cm lies along the base, so it cannot be used as a height.
