Rectangle and Triangle Area - SSAT Middle Level: Quantitative
Card 1 of 25
State the formula for the area of a rectangle with length $l$ and width $w$.
State the formula for the area of a rectangle with length $l$ and width $w$.
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$A = lw$. The area of a rectangle is calculated as the product of its length and width.
$A = lw$. The area of a rectangle is calculated as the product of its length and width.
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Identify the missing height: A triangle has area $24$ and base $8$. What is $h$?
Identify the missing height: A triangle has area $24$ and base $8$. What is $h$?
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$6$. Solve for height by rearranging the formula: $h = \frac{2 \times 24}{8} = 6$.
$6$. Solve for height by rearranging the formula: $h = \frac{2 \times 24}{8} = 6$.
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What is the area of a triangle with $b = 12$ and $h = \frac{1}{2}$?
What is the area of a triangle with $b = 12$ and $h = \frac{1}{2}$?
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$3$. Apply the triangle area formula with fractions: $\frac{1}{2} \times 12 \times \frac{1}{2} = 3$.
$3$. Apply the triangle area formula with fractions: $\frac{1}{2} \times 12 \times \frac{1}{2} = 3$.
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What is the area of a rectangle with $l = \frac{1}{2}$ and $w = 10$?
What is the area of a rectangle with $l = \frac{1}{2}$ and $w = 10$?
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$5$. Multiply the length by the width, including fractions: $\frac{1}{2} \times 10 = 5$.
$5$. Multiply the length by the width, including fractions: $\frac{1}{2} \times 10 = 5$.
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What is the area of a triangle with $b = 7$ and $h = 3.5$?
What is the area of a triangle with $b = 7$ and $h = 3.5$?
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$12.25$. Apply the triangle area formula with decimals: $\frac{1}{2} \times 7 \times 3.5 = 12.25$.
$12.25$. Apply the triangle area formula with decimals: $\frac{1}{2} \times 7 \times 3.5 = 12.25$.
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What is the area of a rectangle with $l = 3.5$ and $w = 6$?
What is the area of a rectangle with $l = 3.5$ and $w = 6$?
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$21$. Multiply the length by the width, handling decimals: $3.5 \times 6 = 21$.
$21$. Multiply the length by the width, handling decimals: $3.5 \times 6 = 21$.
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Identify the missing base: A triangle has area $30$ and height $10$. What is $b$?
Identify the missing base: A triangle has area $30$ and height $10$. What is $b$?
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$6$. Solve for base by rearranging the formula: $b = \frac{2 \times 30}{10} = 6$.
$6$. Solve for base by rearranging the formula: $b = \frac{2 \times 30}{10} = 6$.
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Identify the missing dimension: A rectangle has area $63$ and length $9$. What is $w$?
Identify the missing dimension: A rectangle has area $63$ and length $9$. What is $w$?
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$7$. Divide the area by the length to solve for width: $63 \div 9 = 7$.
$7$. Divide the area by the length to solve for width: $63 \div 9 = 7$.
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Which measurement is used as the height in $A = \frac{1}{2}bh$: the perpendicular distance to the base or any side length?
Which measurement is used as the height in $A = \frac{1}{2}bh$: the perpendicular distance to the base or any side length?
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The perpendicular distance to the base. The height in the triangle area formula must be the perpendicular distance from the base to the opposite vertex.
The perpendicular distance to the base. The height in the triangle area formula must be the perpendicular distance from the base to the opposite vertex.
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What is the area of a rectangle with $l = 7$ and $w = 8$?
What is the area of a rectangle with $l = 7$ and $w = 8$?
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$56$. Multiply the length by the width to find the area: $7 \times 8 = 56$.
$56$. Multiply the length by the width to find the area: $7 \times 8 = 56$.
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What is the area of a rectangle with $l = 12$ and $w = 5$?
What is the area of a rectangle with $l = 12$ and $w = 5$?
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$60$. Multiply the length by the width to find the area: $12 \times 5 = 60$.
$60$. Multiply the length by the width to find the area: $12 \times 5 = 60$.
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What is the area of a rectangle with $l = 9$ and $w = 4$?
What is the area of a rectangle with $l = 9$ and $w = 4$?
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$36$. Multiply the length by the width to find the area: $9 \times 4 = 36$.
$36$. Multiply the length by the width to find the area: $9 \times 4 = 36$.
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State the formula for the area of a triangle with base $b$ and height $h$.
State the formula for the area of a triangle with base $b$ and height $h$.
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$A = \frac{1}{2}bh$. The area of a triangle is half the product of its base and height.
$A = \frac{1}{2}bh$. The area of a triangle is half the product of its base and height.
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What is the area of a triangle with $b = 10$ and $h = 6$?
What is the area of a triangle with $b = 10$ and $h = 6$?
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$30$. Apply the triangle area formula: $\frac{1}{2} \times 10 \times 6 = 30$.
$30$. Apply the triangle area formula: $\frac{1}{2} \times 10 \times 6 = 30$.
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What is the area of a triangle with $b = 9$ and $h = 8$?
What is the area of a triangle with $b = 9$ and $h = 8$?
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$36$. Apply the triangle area formula: $\frac{1}{2} \times 9 \times 8 = 36$.
$36$. Apply the triangle area formula: $\frac{1}{2} \times 9 \times 8 = 36$.
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What is the area of a triangle with $b = 14$ and $h = 5$?
What is the area of a triangle with $b = 14$ and $h = 5$?
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$35$. Apply the triangle area formula: $\frac{1}{2} \times 14 \times 5 = 35$.
$35$. Apply the triangle area formula: $\frac{1}{2} \times 14 \times 5 = 35$.
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Identify the missing dimension: A rectangle has area $48$ and width $6$. What is $l$?
Identify the missing dimension: A rectangle has area $48$ and width $6$. What is $l$?
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$8$. Divide the area by the width to solve for length: $48 \div 6 = 8$.
$8$. Divide the area by the width to solve for length: $48 \div 6 = 8$.
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What is the area of a right triangle with legs $5$ and $12$ (use legs as $b$ and $h$)?
What is the area of a right triangle with legs $5$ and $12$ (use legs as $b$ and $h$)?
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$30$. For a right triangle, use the legs as base and height: $\frac{1}{2} \times 5 \times 12 = 30$.
$30$. For a right triangle, use the legs as base and height: $\frac{1}{2} \times 5 \times 12 = 30$.
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What is the area of a triangle with $b = 16$ and $h = 9$?
What is the area of a triangle with $b = 16$ and $h = 9$?
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$72$. Apply the triangle area formula: $\frac{1}{2} \times 16 \times 9 = 72$.
$72$. Apply the triangle area formula: $\frac{1}{2} \times 16 \times 9 = 72$.
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What is the area of a rectangle with $l = 15$ and $w = 2$?
What is the area of a rectangle with $l = 15$ and $w = 2$?
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$30$. Multiply the length by the width to find the area: $15 \times 2 = 30$.
$30$. Multiply the length by the width to find the area: $15 \times 2 = 30$.
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Find the area: A triangle has $b = 18$ and $h = 4$.
Find the area: A triangle has $b = 18$ and $h = 4$.
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$36$. Apply the triangle area formula: $\frac{1}{2} \times 18 \times 4 = 36$.
$36$. Apply the triangle area formula: $\frac{1}{2} \times 18 \times 4 = 36$.
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Find the area: A rectangle has $l = 11$ and $w = 11$.
Find the area: A rectangle has $l = 11$ and $w = 11$.
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$121$. Multiply the length by the width to find the area: $11 \times 11 = 121$.
$121$. Multiply the length by the width to find the area: $11 \times 11 = 121$.
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Identify the missing width: A rectangle has area $90$ and length $15$. What is $w$?
Identify the missing width: A rectangle has area $90$ and length $15$. What is $w$?
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$6$. Divide the area by the length to solve for width: $90 \div 15 = 6$.
$6$. Divide the area by the length to solve for width: $90 \div 15 = 6$.
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Identify the missing height: A triangle has area $45$ and base $9$. What is $h$?
Identify the missing height: A triangle has area $45$ and base $9$. What is $h$?
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$10$. Solve for height by rearranging the formula: $h = \frac{2 \times 45}{9} = 10$.
$10$. Solve for height by rearranging the formula: $h = \frac{2 \times 45}{9} = 10$.
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Find and correct the error: A student writes triangle area as $A = bh$. What is the correct formula?
Find and correct the error: A student writes triangle area as $A = bh$. What is the correct formula?
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$A = \frac{1}{2}bh$. The student omitted the factor of $\frac{1}{2}$, which accounts for the triangular shape being half of a rectangle with the same base and height.
$A = \frac{1}{2}bh$. The student omitted the factor of $\frac{1}{2}$, which accounts for the triangular shape being half of a rectangle with the same base and height.
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