Testinar Grade 3 math

Area as Additive

Students will find the area of composite figures by decomposing them and adding partial areas.

CH06-09 Geometry and Measurement
Name
Date
Score
____ / 8
Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

  1. A shape is made of two rectangles. Rectangle 1 has area \(12\) sq units, and Rectangle 2 has area \(15\) sq units. What is the total area?

    1. \(15\) sq units
    2. \(24\) sq units
    3. \(27\) sq units
    4. \(180\) sq units

  2. An L-shaped garden is divided into two rectangles. The top rectangle has length \(5\) m and width \(3\) m. The bottom rectangle has length \(4\) m and width \(2\) m. What is the total area of the garden?

    Area as Additive visual for G3-C06-T09-Q002
    1. \(14\) sq m
    2. \(23\) sq m
    3. \(38\) sq m
    4. \(120\) sq m

  3. A composite shape is made by joining two rectangles. What is the total area?

    Area as Additive visual for G3-C06-T09-Q003
    1. \(6\) sq units
    2. \(9\) sq units
    3. \(12\) sq units
    4. \(15\) sq units

  4. A floor plan shows an L-shaped room. One part is \(4\) units long and \(3\) units wide. The other part is \(6\) units long and \(2\) units wide. What is the total floor area?

    Area as Additive visual for G3-C06-T09-Q004
    1. \(24\) sq units
    2. \(18\) sq units
    3. \(12\) sq units
    4. \(36\) sq units

  5. A composite shape has areas of \(18\) sq units and \(11\) sq units. Find the total area.

    Area as Additive visual for G3-C06-T09-Q005
    1. \(29\) sq units
    2. \(18\) sq units
    3. \(7\) sq units
    4. \(198\) sq units

  6. An L-shaped patio is shown with dashed lines dividing it into two rectangles. The first rectangle is \(5\) ft by \(4\) ft. The second is \(3\) ft by \(2\) ft. What is the total area of the patio?

    Area as Additive visual for G3-C06-T09-Q006
    1. \(26\) sq ft
    2. \(20\) sq ft
    3. \(14\) sq ft
    4. \(40\) sq ft

  7. Which shows a correct way to find the total area of an L-shaped figure?

    1. Multiply the length times the width once
    2. Break it into rectangles and add their areas
    3. Multiply the perimeter by 2
    4. Count only the longest parts

  8. An L-shaped garden with dashed decomposition lines shows: The bottom part is \(5\) units by \(2\) units. The top part is \(2\) units by \(2\) units. What is the total area?

    Area as Additive visual for G3-C06-T09-Q009
    1. \(4\) sq units
    2. \(14\) sq units
    3. \(10\) sq units
    4. \(20\) sq units
Teacher and parent reference

Answer key and explanations

  1. C. \(27\) sq units

    When a composite shape is divided into non-overlapping rectangles, the total area equals the sum of the individual rectangle areas. Here: \(12+15=27\) square units.

  2. B. \(23\) sq m

    Find each rectangle: top is \(5 \times 3 = 15\) sq m; bottom is \(4 \times 2 = 8\) sq m. Total: \(15+8=23\) sq m.

  3. B. \(9\) sq units

    Left rectangle: \(3 \times 2 = 6\) sq units. Right rectangle: \(3 \times 1 = 3\) sq units. Total: \(6+3=9\) sq units.

  4. A. \(24\) sq units

    Part 1: \(4 \times 3 = 12\) sq units. Part 2: \(6 \times 2 = 12\) sq units. Total: \(12+12=24\) sq units.

  5. A. \(29\) sq units

    Add the areas: \(18+11=29\) square units. Choice B (only one part) and C (subtraction) are common errors.

  6. A. \(26\) sq ft

    Top rectangle: \(5 \times 4 = 20\) sq ft. Bottom rectangle: \(3 \times 2 = 6\) sq ft. Total: \(20+6=26\) sq ft.

  7. B. Break it into rectangles and add their areas

    Composite shapes are found by dividing them into non-overlapping rectangles, finding each area, and adding them together. Choice A fails because an L-shape is not a single rectangle. Choices C and D are incorrect methods.

  8. B. \(14\) sq units

    Bottom: \(5 \times 2 = 10\) sq units. Top: \(2 \times 2 = 4\) sq units. Total: \(10+4=14\) sq units.

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