6th Grade Math Flashcards: Find Area By Composing And Decomposing

What this deck covers

This deck focuses on Find Area By Composing And Decomposing, giving you a quick way to review the definitions, rules, and examples that matter most for 6th Grade Math.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: A floor section is a trapezoid with bases $8\text{ m}$ and $12\text{ m}$ and height $5\text{ m}$. What area is covered?

Answer: $50\text{ m}^2$. Trapezoid: $\frac{1}{2}(8+12) \times 5 = 50$.

Flashcard 2: What is the area of an $L$-shape made from a $10\times 8$ rectangle with a $4\times 3$ corner removed?

Answer: $68\text{ square units}$. Large rectangle minus removed corner: $80-12=68$.

Flashcard 3: What is the area of a rhombus with diagonals $d_1=10$ and $d_2=6$ units?

Answer: $30\text{ square units}$. Apply $A=\frac{1}{2}d_1d_2$: $\frac{1}{2}(10)(6)=30$.

Flashcard 4: What is the area of a right triangle with legs $6$ and $8$?

Answer: $24$ square units. Right triangle area: $\frac{1}{2} \times 6 \times 8 = 24$.

Flashcard 5: What is the area of a trapezoid with $b_1=6$, $b_2=10$, and $h=5$ square units?

Answer: $40$. Apply $A = \frac{1}{2}(6+10) \times 5 = \frac{1}{2} \times 16 \times 5$.

Flashcard 6: What is the area of a rectangle with $l=11$ and $w=3$ square units?

Answer: $33$. Multiply length by width: $11 \times 3 = 33$.

Flashcard 7: What is the height $h$ of a trapezoid with area $45$ and bases $b_1=5$, $b_2=10$?

Answer: $6$. Solve $45 = \frac{1}{2}(5+10) \times h$ for $h$.

Flashcard 8: State the formula for the area of a triangle using base $b$ and height $h$.

Answer: $A=\frac{1}{2}bh$. Half the base times height gives triangle area.

Flashcard 9: Identify the height to use if a triangle has base $10$ and perpendicular height $7$.

Answer: $h=7$. The perpendicular height is always used in area calculations.

Flashcard 10: What is the height of a parallelogram with area $56$ and base $7$?

Answer: $8$. Solve $56 = 7 \times h$ for $h$.

Flashcard 11: What is the area of a triangle with base $12$ units and height $5$ units?

Answer: $30\text{ square units}$. Apply $A=\frac{1}{2}bh$: $\frac{1}{2}(12)(5)=30$.

Flashcard 12: Which measurement must be perpendicular to the base when finding area with $A=bh$?

Answer: $\text{The height (altitude)}$. Height must form a $90°$ angle with the base.

Flashcard 13: What is the base of a triangle with area $30$ and height $6$?

Answer: $10$. Solve $30 = \frac{1}{2} \times b \times 6$ for $b$.

Flashcard 14: What is the area of a composite shape: a $9\times 6$ rectangle plus a triangle with base $9$ and height $4$?

Answer: $72$. Rectangle $54$ plus triangle $\frac{1}{2} \times 9 \times 4 = 18$.

Flashcard 15: A triangular sign has base $14\text{ cm}$ and height $9\text{ cm}$. What is its area?

Answer: $63\text{ cm}^2$. Apply triangle formula: $\frac{1}{2} \times 14 \times 9$.

Flashcard 16: What is the area of a rhombus with diagonals $12$ and $5$?

Answer: $30$ square units. Apply $\frac{1}{2} \times 12 \times 5 = 30$.

Flashcard 17: What is the area of a composite shape: rectangle $8\times 5$ plus right triangle with legs $4$ and $6$?

Answer: $52\text{ square units}$. Rectangle: $8×5=40$; triangle: $\frac{1}{2}(4)(6)=12$; total: $52$.

Flashcard 18: What is the area of a square with side length $7$ units?

Answer: $49\text{ square units}$. Square area is side squared: $7^2=49$.

Flashcard 19: Identify the correct base-height pair for $A=\frac{1}{2}bh$ in any triangle.

Answer: A base and its perpendicular height. Height must be perpendicular to the chosen base.

Flashcard 20: Find the missing height $h$ of a parallelogram with area $45$ and base $9$.

Answer: $5$. Solve $45 = 9h$ to find height.

Flashcard 21: What is the area of a trapezoid with bases $6$ and $10$ and height $5$?

Answer: $40$ square units. Average bases $(6+10)/2 = 8$, times height $5$.

Flashcard 22: What is the area of a polygon split into two triangles with areas $18$ and $25$ square units?

Answer: $43\text{ square units}$. Add the areas of component shapes: $18+25=43$.

Flashcard 23: What is the area of a right triangle with legs $6$ and $8$ units?

Answer: $24\text{ square units}$. Use $A=\frac{1}{2}bh$ with legs as base and height: $\frac{1}{2}(6)(8)=24$.

Flashcard 24: What is the area of an L-shape formed from a $10\times 8$ rectangle with a $4\times 3$ rectangle removed?

Answer: $68$. Large rectangle $80$ minus small rectangle $12$.

Flashcard 25: State the formula for the area of a kite or rhombus using diagonals $d_1$ and $d_2$.

Answer: $A=\frac{1}{2}d_1d_2$. Half the product of the two diagonals.

Flashcard 26: State the area formula for a triangle using base $b$ and height $h$.

Answer: $A=\frac{1}{2}bh$. Area equals half the product of base and height.

Flashcard 27: What is the area of a right triangle with legs $6$ and $8$ square units?

Answer: $24$. Right triangle area is $\frac{1}{2} \times 6 \times 8 = 24$.

Flashcard 28: What is the area of a trapezoid with $b_1=6$, $b_2=10$, and $h=5$?

Answer: $40\text{ square units}$. Apply formula: $\frac{1}{2}(6+10)(5)=\frac{1}{2}(16)(5)=40$.

Flashcard 29: A triangular sign has base $14\text{ in}$ and height $9\text{ in}$. What is its area?

Answer: $63\text{ in}^2$. Apply $A=\frac{1}{2}bh$: $\frac{1}{2}(14)(9)=63$ square inches.

Flashcard 30: What is the area of an L-shape formed by a $10\times 6$ rectangle with a $4\times 3$ rectangle removed?

Answer: $48$ square units. Large rectangle $(60)$ minus small rectangle $(12)$.

Flashcard 31: What is the area of a parallelogram with base $9$ and height $4$ units?

Answer: $36\text{ square units}$. Apply $A=bh$: $(9)(4)=36$.

Flashcard 32: State the formula for the area of a rectangle with length $l$ and width $w$.

Answer: $A=lw$. Length times width for rectangles.

Flashcard 33: Identify the correct method to find a polygon area when no single formula fits the whole shape.

Answer: $\text{Decompose into known shapes and add areas}$. Break complex shapes into triangles/rectangles to calculate.

Flashcard 34: What is the height of a triangle with area $48$ and base $12$?

Answer: $8$. Solve $48 = \frac{1}{2} \times 12 \times h$ for $h$.

Flashcard 35: State the area formula for a parallelogram with base $b$ and height $h$.

Answer: $A=bh$. Parallelogram area is base times perpendicular height.

Flashcard 36: A rectangle is split by a diagonal into two congruent triangles. If the rectangle area is $50$, what is one triangle's area?

Answer: $25$ square units. Diagonal splits rectangle into two equal triangles.

Flashcard 37: Identify the height to use if a triangle has base $10$ and a perpendicular height of $7$.

Answer: $7$. Use the perpendicular distance from base to opposite vertex.

Flashcard 38: State the formula for the area of a trapezoid with bases $b_1,b_2$ and height $h$.

Answer: $A=\frac{1}{2}(b_1+b_2)h$. Average the parallel bases, then multiply by height.

Flashcard 39: What is the area of a square with side length $9$ square units?

Answer: $81$. Square area is side squared: $9^2 = 81$.

Flashcard 40: What is the area of a parallelogram with base $9$ and height $4$ square units?

Answer: $36$. Multiply base by height: $9 \times 4 = 36$.

Flashcard 41: Find the missing height $h$ of a trapezoid with area $48$ and bases $10$ and $6$.

Answer: $6$. Solve $48 = \frac{1}{2}(10+6)h = 8h$ for $h$.

Flashcard 42: A floor is a rectangle $12\text{ ft}\times 9\text{ ft}$. What is its area in $\text{ft}^2$?

Answer: $108\text{ ft}^2$. Apply $A=lw$: $(12)(9)=108$ square feet.

Flashcard 43: What is the area of a triangle with base $10$ and height $7$ square units?

Answer: $35$. Apply $A = \frac{1}{2}bh = \frac{1}{2} \times 10 \times 7$.

Flashcard 44: State the area formula for a trapezoid with bases $b_1,b_2$ and height $h$.

Answer: $A=\frac{1}{2}(b_1+b_2)h$. Average the parallel bases, then multiply by height.

Flashcard 45: State the formula for the area of a parallelogram with base $b$ and height $h$.

Answer: $A=bh$. Base times perpendicular height for parallelograms.

Flashcard 46: State the area formula for a kite or rhombus using diagonals $d_1$ and $d_2$.

Answer: $A=\frac{1}{2}d_1d_2$. Half the product of the two diagonals gives the area.

Flashcard 47: What is the area of a composite shape made of a $6\times 4$ rectangle plus a right triangle with legs $4$ and $3$?

Answer: $30$ square units. Rectangle $(24)$ plus triangle $(6)$ equals $30$.

Flashcard 48: What is the area of a rhombus with diagonals $d_1=12$ and $d_2=5$ square units?

Answer: $30$. Apply $A = \frac{1}{2} \times 12 \times 5 = 30$.

Flashcard 49: What is the area of a triangle with base $12$ and height $5$?

Answer: $30$ square units. Apply $A = \frac{1}{2}bh = \frac{1}{2} \times 12 \times 5$.

Flashcard 50: What is the area of a parallelogram with base $9$ and height $4$?

Answer: $36$ square units. Multiply base by perpendicular height: $9 \times 4$.

Flashcard 51: Find the missing height $h$ of a triangle with area $36$ and base $12$.

Answer: $6$. Solve $36 = \frac{1}{2} \times 12 \times h$ for $h$.