ISEE Middle Level Quantitative Reasoning Flashcards: Area Perimeter And Volume

What this deck covers

This deck focuses on Area Perimeter And Volume, giving you a quick way to review the definitions, rules, and examples that matter most for ISEE Middle Level Quantitative Reasoning.

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: What is the area of a trapezoid with $b_1=8$, $b_2=12$, and $h=5$?

Answer: $50$. Average the bases and multiply by height for the trapezoid area.

Flashcard 2: What is the area of a square with perimeter $P=36$?

Answer: $81$. Divide perimeter by 4 to find side length, then square it for area.

Flashcard 3: What is the height $h$ of a triangle with area $A=30$ and base $b=12$?

Answer: $5$. Solve $A = \frac{1}{2}bh$ for $h$ by multiplying area by 2 and dividing by base.

Flashcard 4: State the formula for the area of a trapezoid with bases $b_1,b_2$ and height $h$.

Answer: A = rac{1}{2}(b_1+b_2)h. The area uses the average of the two bases multiplied by the height.

Flashcard 5: What is the volume of a pyramid with base area $B=27$ and height $h=9$?

Answer: $81$. Apply one-third of base area times height for the pyramid volume.

Flashcard 6: What is the volume of a cylinder with $r=2$ and $h=10$? Leave the answer in terms of $\text{\pi}$.

Answer: $40\text{\pi}$. Multiply the base area $\pi r^2$ by height for the cylinder volume.

Flashcard 7: State the formula for the area of a parallelogram with base $b$ and height $h$.

Answer: $A = bh$. The area is the product of the base and corresponding height in the parallelogram.

Flashcard 8: What is the area of a circle with radius $r=3$? Leave the answer in terms of $\text{\pi}$.

Answer: $9\text{\pi}$. Square the radius and multiply by $\pi$ for the circle area.

Flashcard 9: What is the area of a triangle with $b=14$ and $h=6$?

Answer: $42$. Use half the product of base and height for the triangle area.

Flashcard 10: State the formula for the area of a rectangle with length $l$ and width $w$.

Answer: $A = lw$. The area is calculated by multiplying the length by the width to cover the rectangular region.

Flashcard 11: What is the width $w$ of a rectangle with perimeter $P=50$ and length $l=15$?

Answer: $10$. Solve $P = 2l + 2w$ for $w$ by subtracting $2l$ from $P$ and dividing by 2.

Flashcard 12: What is the perimeter of a rectangle with $l=9$ and $w=4$?

Answer: $26$. Apply the perimeter formula $P = 2l + 2w$ with given dimensions.

Flashcard 13: State the formula for the perimeter of a rectangle with length $l$ and width $w$.

Answer: $P = 2l + 2w$. The perimeter sums all sides of the rectangle, equivalent to twice the length plus twice the width.

Flashcard 14: State the formula for the volume of a triangular prism with triangle area $B$ and length $L$.

Answer: $V = BL$. The volume extrudes the triangular base area along the prism's length.

Flashcard 15: What is the area of a rectangle with $l=12$ and $w=5$?

Answer: $60$. Multiply length by width using the rectangle area formula.

Flashcard 16: State the formula for the volume of a cylinder with radius $r$ and height $h$.

Answer: $V = ext{\pi}r^2h$. The volume multiplies the circular base area by the height.

Flashcard 17: What is the circumference of a circle with radius $r=7$? Leave the answer in terms of $\text{\pi}$.

Answer: $14\text{\pi}$. Multiply twice $\pi$ by the radius for the circumference.

Flashcard 18: State the formula for the volume of a pyramid with base area $B$ and height $h$.

Answer: V = rac{1}{3}Bh. The volume takes one-third of the base area times the height due to the tapering shape.

Flashcard 19: State the formula for the area of a triangle with base $b$ and height $h$.

Answer: A = rac{1}{2}bh. The area derives from half the product of the base and height, accounting for the triangular shape.

Flashcard 20: State the formula for the area of a circle with radius $r$.

Answer: $A = ext{\pi}r^2$. The area fills the circle using $\pi$ times the radius squared.

Flashcard 21: State the formula for the volume of a cube with side length $s$.

Answer: $V = s^3$. The volume cubes the side length since all dimensions are equal.

Flashcard 22: What is the volume of a cube with side length $s=6$?

Answer: $216$. Cube the side length to find the cube's volume.

Flashcard 23: State the formula for the circumference of a circle with radius $r$.

Answer: $C = 2 ext{\pi}r$. The circumference measures the circle's boundary as twice the product of $\pi$ and the radius.

Flashcard 24: State the formula for the volume of a rectangular prism with dimensions $l,w,h$.

Answer: $V = lwh$. The volume is the product of length, width, and height to fill the prism.

Flashcard 25: What is the volume of a rectangular prism with $l=8$, $w=3$, and $h=5$?

Answer: $120$. Multiply length, width, and height for the prism volume.