A foundational geometry lesson focusing on decomposing composite two-dimensional figures into familiar shapes (rectangles, squares, parallelograms, and triangles) to calculate total area.
Common Error Watch: Watch for students forgetting to divide by 2 for triangle areas, or confusing the slanted side with the perpendicular height in parallelograms.
Teacher Key • Page 2 Subtotal: 9 Points (15 Points Grand Total) Page 2 of 2
Total Area
+ +
Total = \(\text{ft}^2\)
Problem 4 Decompose into 1 Parallelogram, 1 Rectangle & 1 Triangle
8 in h=3 in 4 in h=3 in S1 S2 S3
Shape 1: Parallelogram
Work:
\(A_1 =\) \(\text{in}^2\)
Shape 2: Rectangle
Work:
\(A_2 =\) \(\text{in}^2\)
Shape 3: Triangle
Work:
\(A_3 =\) \(\text{in}^2\)
Total Area
+ +
Total = \(\text{in}^2\)
Problem 5 Decompose into 1 Triangle, 1 Rectangle & 1 Square
h=4 yd b=12 yd 6×3 yd 9×2 yd S1 S2 S3
Shape 1: Triangle (Head)
Work:
\(A_1 =\) \(\text{yd}^2\)
Shape 2: Rectangle (Shaft)
Work:
\(A_2 =\) \(\text{yd}^2\)
Shape 3: Rectangle (Base)
Work:
\(A_3 =\) \(\text{yd}^2\)
Total Area
+ +
Total = \(\text{yd}^2\)
Strategy: Label each sub-shape (S1, S2, S3) directly on the figure before substituting into the area formulas.
Geometry Practice • 3-Shape Figures Page 2 of 2
\(A_1 = \mathbf{12}\text{ ft}^2\)
Shape 2: Square (Main)
Work: \(6 \times 6 = 6^2\)
\(A_2 = \mathbf{36}\text{ ft}^2\)
Shape 3: Rectangle (Wing)
Work: \(5 \times 6\)
\(A_3 = \mathbf{30}\text{ ft}^2\)
Total Area
\(12 + 36 + 30\)
Total = \(\mathbf{78}\text{ ft}^2\)
Problem 4 Answer Parallelogram + Rectangle + Triangle
4 Points Total
8 in h=3 in 4 in h=3 in S1 S2 S3
Shape 1: Parallelogram
Work: \(8 \times 3\)
\(A_1 = \mathbf{24}\text{ in}^2\)
Shape 2: Rectangle
Work: \(8 \times 4\)
\(A_2 = \mathbf{32}\text{ in}^2\)
Shape 3: Triangle
Work: \(\frac{1}{2}(8)(3)\)
\(A_3 = \mathbf{12}\text{ in}^2\)
Total Area
\(24 + 32 + 12\)
Total = \(\mathbf{68}\text{ in}^2\)
Problem 5 Answer Triangle + Rectangle + Rectangle
4 Points Total
h=4 yd b=12 yd 6×3 yd 9×2 yd S1 S2 S3
Shape 1: Triangle (Head)
Work: \(\frac{1}{2}(12)(4)\)
\(A_1 = \mathbf{24}\text{ yd}^2\)
Shape 2: Rectangle (Shaft)
Work: \(6 \times 3\)
\(A_2 = \mathbf{18}\text{ yd}^2\)
Shape 3: Rectangle (Base)
Work: \(9 \times 2\)
\(A_3 = \mathbf{18}\text{ yd}^2\)
Total Area
\(24 + 18 + 18\)
Total = \(\mathbf{60}\text{ yd}^2\)
Grading Note: Award 1 point for each correctly calculated sub-shape area (work + value) and 1 point for the final sum with units.
