Area of Polygons Worksheet Answer Key – Grade 6

Problem 1 Area of a rectangle

Area = length × width = 14 × 6 = 84.

84 square feet

Problem 2 Area of a parallelogram

Use the perpendicular height, 7 inches. A = bh = 12 × 7 = 84.

84 square inches

Problem 3 Area of a triangle

A = 12 × 16 × 5 = 8 × 5 = 40.

40 square meters

Problem 4 Area of a right triangle

The legs are the base and height. A = 12 × 8 × 15 = 4 × 15 = 60.

60 square feet

Problem 5 Area of a trapezoid

A = 12 (5 + 9) × 6 = 12 × 14 × 6 = 7 × 6 = 42.

42 square meters

Problem 6 Missing height of a triangle

48 = 12 × 16 × h = 8h, so h = 48 ÷ 8 = 6. Check: 12 × 16 × 6 = 48.

6 inches

Problem 7 Missing base of a parallelogram

117 = b × 9, so b = 117 ÷ 9 = 13. Check: 13 × 9 = 117.

13 feet

Problem 8 Trapezoid with a figure

A = 12 (7 + 13) × 8 = 10 × 8 = 80.

80 square meters

Problem 9 Rhombus in four triangles

Each triangle has legs of 5 and 12 (half of each diagonal): 12 × 5 × 12 = 30. Four triangles: 4 × 30 = 120. Check: 12 × 10 × 24 = 120.

30 square inches for one triangle; 120 square inches for the rhombus

Problem 10 L-shaped patio

Split the patio into a 15 by 6 rectangle and a 7 by 4 rectangle, since 10 − 6 = 4 and the top width is 7.

90 + 28 = 118. Check by subtraction: 15 × 10 = 150 and the notch is 8 × 4 = 32, so 150 − 32 = 118.

118 square meters

Problem 11 Obtuse triangle

The height is the perpendicular distance, 9 meters, even though it lies outside the triangle. A = 12 × 14 × 9 = 7 × 9 = 63.

63 square meters

Problem 12 Deck shaped like a trapezoid

A = 12 (12 + 20) × 9 = 16 × 9 = 144.

144 square feet

Problem 13 Triangle or rectangle?

Triangle: 12 × 15 × 8 = 60. Rectangle: 6 × 9 = 54. The difference is 60 − 54 = 6.

The triangle is greater by 6 square feet

Problem 14 House shape

Rectangle: 10 × 6 = 60. Triangle roof: 12 × 10 × 4 = 20. Total: 60 + 20 = 80.

80 square feet

Problem 15 Painting a mural wall

1. A = 12 (24 + 16) × 10 = 20 × 10 = 200 square feet.
2. Two coats cover 2 × 200 = 400 square feet. 400 ÷ 40 = 10 quarts.
3. 10 × 14.50 = 145.

(a) 200 square feet; (b) 10 quarts; (c) $145

Problem 16 Laying sod

1. Split into 30 by 12 and 18 by 8 rectangles: 360 + 144 = 504. Check: 30 × 20 − 12 × 8 = 600 − 96 = 504.
2. 504 ÷ 36 = 14.
3. 14 × 4.25 = 59.50.

(a) 504 square feet; (b) 14 rolls; (c) $59.50

Problem 17 Sails for a sailboat

1. First sail: 12 × 6 × 11 = 33. Second sail: 12 × 5 × 9 = 22.5. Total area 55.5 square meters.
2. 55.5 × 18 = 999.

(a) 33 square meters and 22.5 square meters; (b) $999

Problem 18 Quilt block

1. 24 × 24 = 576.
2. Each corner triangle has legs of 12 and 12: 12 × 12 × 12 = 72.
3. The four corners total 4 × 72 = 288, so the diamond is 576 − 288 = 288. Check: 12 × 24 × 24 = 288.

(a) 576 square inches; (b) 72 square inches; (c) 288 square inches

Problem 19 Painting a barn wall

1. Rectangle: 24 × 12 = 288. Gable: 12 × 24 × 7 = 84. Door: 8 × 9 = 72. Painted area: 288 + 84 − 72 = 300.
2. 300 ÷ 150 = 2.

(a) 300 square feet; (b) 2 gallons

Problem 20 Finding a trapezoid height

Trapezoid: 91 = 12 (8 + 18) × h = 13h, so h = 91 ÷ 13 = 7. Triangle: 91 = 12 × 14 × h = 7h, so h = 91 ÷ 7 = 13.

Trapezoid height 7 meters; triangle height 13 meters