Area, Perimeter, and Volume - ISEE Middle Level: Quantitative Reasoning

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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