Find Area by Composing and Decomposing - 6th Grade Math
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What is the area of a composite shape: rectangle $8\times 5$ plus right triangle with legs $4$ and $6$?
What is the area of a composite shape: rectangle $8\times 5$ plus right triangle with legs $4$ and $6$?
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$52\text{ square units}$. Rectangle: $8×5=40$; triangle: $\frac{1}{2}(4)(6)=12$; total: $52$.
$52\text{ square units}$. Rectangle: $8×5=40$; triangle: $\frac{1}{2}(4)(6)=12$; total: $52$.
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What is the area of an $L$-shape made from a $10\times 8$ rectangle with a $4\times 3$ corner removed?
What is the area of an $L$-shape made from a $10\times 8$ rectangle with a $4\times 3$ corner removed?
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$68\text{ square units}$. Large rectangle minus removed corner: $80-12=68$.
$68\text{ square units}$. Large rectangle minus removed corner: $80-12=68$.
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What is the area of a polygon split into two triangles with areas $18$ and $25$ square units?
What is the area of a polygon split into two triangles with areas $18$ and $25$ square units?
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$43\text{ square units}$. Add the areas of component shapes: $18+25=43$.
$43\text{ square units}$. Add the areas of component shapes: $18+25=43$.
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Identify the correct method to find a polygon area when no single formula fits the whole shape.
Identify the correct method to find a polygon area when no single formula fits the whole shape.
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$\text{Decompose into known shapes and add areas}$. Break complex shapes into triangles/rectangles to calculate.
$\text{Decompose into known shapes and add areas}$. Break complex shapes into triangles/rectangles to calculate.
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A floor is a rectangle $12\text{ ft}\times 9\text{ ft}$. What is its area in $\text{ft}^2$?
A floor is a rectangle $12\text{ ft}\times 9\text{ ft}$. What is its area in $\text{ft}^2$?
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$108\text{ ft}^2$. Apply $A=lw$: $(12)(9)=108$ square feet.
$108\text{ ft}^2$. Apply $A=lw$: $(12)(9)=108$ square feet.
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What is the area of a triangle with base $12$ units and height $5$ units?
What is the area of a triangle with base $12$ units and height $5$ units?
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$30\text{ square units}$. Apply $A=\frac{1}{2}bh$: $\frac{1}{2}(12)(5)=30$.
$30\text{ square units}$. Apply $A=\frac{1}{2}bh$: $\frac{1}{2}(12)(5)=30$.
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What is the area of a right triangle with legs $6$ and $8$ units?
What is the area of a right triangle with legs $6$ and $8$ units?
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$24\text{ square units}$. Use $A=\frac{1}{2}bh$ with legs as base and height: $\frac{1}{2}(6)(8)=24$.
$24\text{ square units}$. Use $A=\frac{1}{2}bh$ with legs as base and height: $\frac{1}{2}(6)(8)=24$.
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Which measurement must be perpendicular to the base when finding area with $A=bh$?
Which measurement must be perpendicular to the base when finding area with $A=bh$?
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$\text{The height (altitude)}$. Height must form a $90°$ angle with the base.
$\text{The height (altitude)}$. Height must form a $90°$ angle with the base.
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What is the area of a rhombus with diagonals $d_1=10$ and $d_2=6$ units?
What is the area of a rhombus with diagonals $d_1=10$ and $d_2=6$ units?
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$30\text{ square units}$. Apply $A=\frac{1}{2}d_1d_2$: $\frac{1}{2}(10)(6)=30$.
$30\text{ square units}$. Apply $A=\frac{1}{2}d_1d_2$: $\frac{1}{2}(10)(6)=30$.
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State the area formula for a kite or rhombus using diagonals $d_1$ and $d_2$.
State the area formula for a kite or rhombus using diagonals $d_1$ and $d_2$.
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$A=\frac{1}{2}d_1d_2$. Half the product of the two diagonals gives the area.
$A=\frac{1}{2}d_1d_2$. Half the product of the two diagonals gives the area.
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What is the area of a square with side length $7$ units?
What is the area of a square with side length $7$ units?
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$49\text{ square units}$. Square area is side squared: $7^2=49$.
$49\text{ square units}$. Square area is side squared: $7^2=49$.
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What is the area of a trapezoid with $b_1=6$, $b_2=10$, and $h=5$?
What is the area of a trapezoid with $b_1=6$, $b_2=10$, and $h=5$?
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$40\text{ square units}$. Apply formula: $\frac{1}{2}(6+10)(5)=\frac{1}{2}(16)(5)=40$.
$40\text{ square units}$. Apply formula: $\frac{1}{2}(6+10)(5)=\frac{1}{2}(16)(5)=40$.
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State the area formula for a trapezoid with bases $b_1,b_2$ and height $h$.
State the area formula for a trapezoid with bases $b_1,b_2$ and height $h$.
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$A=\frac{1}{2}(b_1+b_2)h$. Average the parallel bases, then multiply by height.
$A=\frac{1}{2}(b_1+b_2)h$. Average the parallel bases, then multiply by height.
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What is the area of a parallelogram with base $9$ and height $4$ units?
What is the area of a parallelogram with base $9$ and height $4$ units?
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$36\text{ square units}$. Apply $A=bh$: $(9)(4)=36$.
$36\text{ square units}$. Apply $A=bh$: $(9)(4)=36$.
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State the area formula for a parallelogram with base $b$ and height $h$.
State the area formula for a parallelogram with base $b$ and height $h$.
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$A=bh$. Parallelogram area is base times perpendicular height.
$A=bh$. Parallelogram area is base times perpendicular height.
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Identify the height to use if a triangle has base $10$ and perpendicular height $7$.
Identify the height to use if a triangle has base $10$ and perpendicular height $7$.
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$h=7$. The perpendicular height is always used in area calculations.
$h=7$. The perpendicular height is always used in area calculations.
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State the area formula for a triangle using base $b$ and height $h$.
State the area formula for a triangle using base $b$ and height $h$.
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$A=\frac{1}{2}bh$. Area equals half the product of base and height.
$A=\frac{1}{2}bh$. Area equals half the product of base and height.
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A triangular sign has base $14\text{ in}$ and height $9\text{ in}$. What is its area?
A triangular sign has base $14\text{ in}$ and height $9\text{ in}$. What is its area?
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$63\text{ in}^2$. Apply $A=\frac{1}{2}bh$: $\frac{1}{2}(14)(9)=63$ square inches.
$63\text{ in}^2$. Apply $A=\frac{1}{2}bh$: $\frac{1}{2}(14)(9)=63$ square inches.
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What is the height of a parallelogram with area $56$ and base $7$?
What is the height of a parallelogram with area $56$ and base $7$?
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$8$. Solve $56 = 7 \times h$ for $h$.
$8$. Solve $56 = 7 \times h$ for $h$.
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What is the area of a trapezoid with $b_1=6$, $b_2=10$, and $h=5$ square units?
What is the area of a trapezoid with $b_1=6$, $b_2=10$, and $h=5$ square units?
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$40$. Apply $A = \frac{1}{2}(6+10) \times 5 = \frac{1}{2} \times 16 \times 5$.
$40$. Apply $A = \frac{1}{2}(6+10) \times 5 = \frac{1}{2} \times 16 \times 5$.
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What is the area of a rhombus with diagonals $d_1=12$ and $d_2=5$ square units?
What is the area of a rhombus with diagonals $d_1=12$ and $d_2=5$ square units?
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$30$. Apply $A = \frac{1}{2} \times 12 \times 5 = 30$.
$30$. Apply $A = \frac{1}{2} \times 12 \times 5 = 30$.
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What is the area of a rectangle with $l=11$ and $w=3$ square units?
What is the area of a rectangle with $l=11$ and $w=3$ square units?
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$33$. Multiply length by width: $11 \times 3 = 33$.
$33$. Multiply length by width: $11 \times 3 = 33$.
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Identify the correct base-height pair for $A=\frac{1}{2}bh$ in any triangle.
Identify the correct base-height pair for $A=\frac{1}{2}bh$ in any triangle.
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A base and its perpendicular height. Height must be perpendicular to the chosen base.
A base and its perpendicular height. Height must be perpendicular to the chosen base.
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What is the height of a triangle with area $48$ and base $12$?
What is the height of a triangle with area $48$ and base $12$?
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$8$. Solve $48 = \frac{1}{2} \times 12 \times h$ for $h$.
$8$. Solve $48 = \frac{1}{2} \times 12 \times h$ for $h$.
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What is the base of a triangle with area $30$ and height $6$?
What is the base of a triangle with area $30$ and height $6$?
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$10$. Solve $30 = \frac{1}{2} \times b \times 6$ for $b$.
$10$. Solve $30 = \frac{1}{2} \times b \times 6$ for $b$.
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