Find Area of Composite Figures - 3rd Grade Math
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What is the area of a $6 \times 6$ square in square units?
What is the area of a $6 \times 6$ square in square units?
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$36$ square units. Square area equals side squared: $6 \times 6 = 36$.
$36$ square units. Square area equals side squared: $6 \times 6 = 36$.
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What is the area formula for a rectangle with side lengths $l$ and $w$?
What is the area formula for a rectangle with side lengths $l$ and $w$?
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$A = l \times w$. Multiply length times width to find rectangular area.
$A = l \times w$. Multiply length times width to find rectangular area.
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Find the area of a rectilinear figure decomposed into $5 \times 2$ and $5 \times 3$ rectangles.
Find the area of a rectilinear figure decomposed into $5 \times 2$ and $5 \times 3$ rectangles.
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$25$ square units. Add areas: $(5 \times 2) + (5 \times 3) = 10 + 15 = 25$.
$25$ square units. Add areas: $(5 \times 2) + (5 \times 3) = 10 + 15 = 25$.
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What does it mean that area is additive for non-overlapping rectangles?
What does it mean that area is additive for non-overlapping rectangles?
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Total area $=$ sum of the parts’ areas. Areas of separate parts can be added together to find the whole.
Total area $=$ sum of the parts’ areas. Areas of separate parts can be added together to find the whole.
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A floor section is $8 \text{ ft}$ by $3 \text{ ft}$. What is its area in $\text{ft}^2$?
A floor section is $8 \text{ ft}$ by $3 \text{ ft}$. What is its area in $\text{ft}^2$?
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$24\ \text{ft}^2$. Multiply dimensions: $8 \times 3 = 24$ square feet.
$24\ \text{ft}^2$. Multiply dimensions: $8 \times 3 = 24$ square feet.
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A garden is made of two rectangles: $4 \text{ m} \times 5 \text{ m}$ and $2 \text{ m} \times 5 \text{ m}$. Find total area.
A garden is made of two rectangles: $4 \text{ m} \times 5 \text{ m}$ and $2 \text{ m} \times 5 \text{ m}$. Find total area.
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$30\ \text{m}^2$. Add areas: $(4 \times 5) + (2 \times 5) = 20 + 10 = 30$.
$30\ \text{m}^2$. Add areas: $(4 \times 5) + (2 \times 5) = 20 + 10 = 30$.
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What is the total area of a $7 \times 4$ rectangle if it is decomposed into $7 \times 1$ and $7 \times 3$?
What is the total area of a $7 \times 4$ rectangle if it is decomposed into $7 \times 1$ and $7 \times 3$?
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$28$ square units. Verify: $(7 \times 1) + (7 \times 3) = 7 + 21 = 28 = 7 \times 4$.
$28$ square units. Verify: $(7 \times 1) + (7 \times 3) = 7 + 21 = 28 = 7 \times 4$.
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Choose the expression for total area of two rectangles with areas $a$ and $b$ (no overlap).
Choose the expression for total area of two rectangles with areas $a$ and $b$ (no overlap).
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$a + b$. Non-overlapping areas are simply added together.
$a + b$. Non-overlapping areas are simply added together.
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Find the area of a figure split into $3$ rectangles: $2 \times 4$, $1 \times 4$, and $3 \times 2$.
Find the area of a figure split into $3$ rectangles: $2 \times 4$, $1 \times 4$, and $3 \times 2$.
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$18$ square units. Add areas: $(2 \times 4) + (1 \times 4) + (3 \times 2) = 8 + 4 + 6 = 18$.
$18$ square units. Add areas: $(2 \times 4) + (1 \times 4) + (3 \times 2) = 8 + 4 + 6 = 18$.
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Find the area of an L-shape split into rectangles $4 \times 3$ and $2 \times 3$ (non-overlapping).
Find the area of an L-shape split into rectangles $4 \times 3$ and $2 \times 3$ (non-overlapping).
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$18$ square units. Add areas: $(4 \times 3) + (2 \times 3) = 12 + 6 = 18$.
$18$ square units. Add areas: $(4 \times 3) + (2 \times 3) = 12 + 6 = 18$.
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Find the area of a rectilinear figure made of $2$ rectangles: $3 \times 7$ and $2 \times 7$ (non-overlapping).
Find the area of a rectilinear figure made of $2$ rectangles: $3 \times 7$ and $2 \times 7$ (non-overlapping).
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$35$ square units. Add areas: $(3 \times 7) + (2 \times 7) = 21 + 14 = 35$.
$35$ square units. Add areas: $(3 \times 7) + (2 \times 7) = 21 + 14 = 35$.
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Which method matches additive area: add the areas of parts or add the perimeters of parts?
Which method matches additive area: add the areas of parts or add the perimeters of parts?
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Add the areas of parts. Area is additive; perimeter is not for composite figures.
Add the areas of parts. Area is additive; perimeter is not for composite figures.
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Identify the error: A student adds areas of two rectangles that overlap. What is wrong?
Identify the error: A student adds areas of two rectangles that overlap. What is wrong?
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The overlap is counted twice. Overlapping areas violate the non-overlapping requirement.
The overlap is counted twice. Overlapping areas violate the non-overlapping requirement.
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Find the missing part area if total area is $35$ and one rectangle part is $20$ square units.
Find the missing part area if total area is $35$ and one rectangle part is $20$ square units.
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$15$ square units. Subtract known part from total: $35 - 20 = 15$.
$15$ square units. Subtract known part from total: $35 - 20 = 15$.
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Find the total area: rectangle $A$ is $2 \times 9$ and rectangle $B$ is $3 \times 4$ (non-overlapping).
Find the total area: rectangle $A$ is $2 \times 9$ and rectangle $B$ is $3 \times 4$ (non-overlapping).
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$30$ square units. Add areas: $(2 \times 9) + (3 \times 4) = 18 + 12 = 30$.
$30$ square units. Add areas: $(2 \times 9) + (3 \times 4) = 18 + 12 = 30$.
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