Area and Perimeter (Advanced) — Answer Key
Part A: Multiple Choice
Circle the best answer for each question.
1. An L-shape splits into a 6 by 4 rectangle and a 3 by 2 rectangle. What is its total area?
A) 30 square units
B) 24 square units
C) 18 square units
D) 32 square units
6 x 4 = 24 and 3 x 2 = 6, so 24 + 6 equals 30 square units after decomposition.
2. A T-shape decomposes into a 8 by 2 top bar and a 2 by 5 stem. What is its area?
A) 26 square units
B) 21 square units
C) 16 square units
D) 40 square units
Top bar 8 x 2 = 16; stem 2 x 5 = 10; total area is 16 + 10 = 26 square units.
3. A plus shape is made of a 3 by 9 horizontal bar and a 9 by 3 vertical bar that overlap on a 3 by 3 center. What is its area?
A) 45 square units
B) 54 square units
C) 27 square units
D) 63 square units
3 x 9 = 27 twice gives 54, but the 3 x 3 = 9 overlap is counted twice, so 54 - 9 = 45 square units.
4. A compound shape decomposes into rectangles of 5 by 4, 3 by 2, and 6 by 1. What is the total area?
A) 32 square units
B) 29 square units
C) 26 square units
D) 20 square units
20 + 6 + 6 = 32 square units; decomposing complex shapes into rectangles makes the area additive.
Part B: Fill in the Blank
Write the correct answer on each line.
1. To find the area of an L-shape, you decompose it into rectangles.
Decompose means to split a complex shape into simple rectangles whose areas can be added.
2. An L-shape with parts 6 by 4 and 3 by 2 has total area 30 square units.
Each rectangle's dimensions multiply to 24 and 6, summing to 30 square units.
3. When two bars of a plus shape overlap, you must subtract the overlap once.
The overlap is counted in both bars, so subtracting once corrects the total area.
4. A T-shape with a 8 by 2 top and 2 by 5 stem has area 26 square units.
Top bar 16 plus stem 10 equals 26 square units when no parts overlap.
5. Compound shape areas are always reported in square units.
Whether the shape is L, T, or plus, areas combine length and width into square units.