Area and Perimeter (Advanced) — Answer Key
Part A: Multiple Choice
Circle the best answer for each question.
1. A rectangle has perimeter 30 ft and length 9 ft. What is the width?
A) 3 ft
B) 5 ft
C) 6 ft
D) 12 ft
Grade 4: 30 - 2(9) = 30 - 18 = 12; 12 / 2 = 6 ft.
2. A T-shape has a 6 m by 3 m rectangle and a 4 m by 2 m rectangle. Total area?
A) 18 sq m
B) 22 sq m
C) 26 sq m
D) 30 sq m
Grade 4: 18 + 8 = 26 sq m.
3. A rectangle has area 100 sq cm and width 10 cm. What is the perimeter?
A) 20 cm
B) 30 cm
C) 40 cm
D) 50 cm
Grade 4: length = 100 / 10 = 10 cm; perimeter = 2(10) + 2(10) = 40 cm.
4. Which compound shape has the larger area: A) two 5x4 rectangles, or B) one 6x7 rectangle plus a 2x2 square?
A) A is larger
B) B is larger
C) They are equal
D) Cannot tell
Grade 4: A = 20 + 20 = 40; B = 42 + 4 = 46. B is larger.
Part B: Fill in the Blank
Write the correct answer on each line.
1. A rectangle has perimeter 40 m and width 8 m. The length is 12 meters.
Grade 4: 40 - 2(8) = 24; 24 / 2 = 12 m.
2. An L-shape has a 9 ft by 5 ft rectangle and a 4 ft by 3 ft rectangle. The total area is 57 square feet.
Grade 4: 9 x 5 = 45 and 4 x 3 = 12; 45 + 12 = 57 sq ft.
3. A rectangle has area 84 sq in and length 12 in. The width is 7 inches.
Grade 4: 84 / 12 = 7 in.
4. A square has perimeter 32 cm. Its area is 64 square centimeters.
Grade 4: side = 32 / 4 = 8 cm; area = 8 x 8 = 64 sq cm.
5. A T-shape has a 10 m by 4 m rectangle and a 5 m by 3 m rectangle. The total area is 55 square meters.
Grade 4: 10 x 4 = 40 and 5 x 3 = 15; 40 + 15 = 55 sq m.