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Part of step 20 of 20·Geometry and Trigonometry·Area and Volume Prev
Math

Area and Perimeter

4 min readEasy10-question checkpoint

Area and perimeter questions are formula plug-ins — but the SAT loves to combine shapes (a rectangle with a semicircle on top, a triangle inside a rectangle) so you have to break compound figures into parts.

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Common 2D shapes — area and perimeter
ShapeAreaPerimeter / Circumference
Rectangle (l × w)$lw$$2l + 2w$
Square (side $s$)$s^2$$4s$
Triangle (base $b$, height $h$)$\frac{1}{2}bh$Sum of three sides
Parallelogram$bh$Sum of four sides
Trapezoid (bases $b_1$, $b_2$)$\frac{1}{2}(b_1 + b_2)h$Sum of four sides
Circle (radius $r$)$\pi r^2$$2\pi r$
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How to handle a compound shape
Is the shape a single recognized figure (rectangle / circle / triangle)?
Yes ↓
Use the standard formula directly
No ↓
Can you DECOMPOSE the shape into pieces (e.g., rectangle + semicircle)?
Yes ↓
Are pieces ADDED to make the shape, or SUBTRACTED (cut out)?
Yes ↓
ADD if the pieces combine to make the shape; SUBTRACT if part is cut away
No ↓
Compute each piece, then choose the right operation based on the figure
No ↓
Look for the OUTER region minus an INNER region — most compound figures are one shape with another removed
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Quick check

Decompose compound shapes into known pieces. Compute each piece. Add or subtract per the figure. Watch radius/diameter and remember the $\frac{1}{2}$ for triangles and trapezoids.

A rectangular garden has a length of 12 meters and a width of 5 meters. What is the area, in square meters, of the garden?

Enter a whole number, fraction (e.g. 3/4), or decimal (e.g. .75).

Worked examples

Example 1
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Example 2
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Common pitfalls

Using the wrong height for a triangle
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Including internal segments in perimeter
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Confusing diameter with radius in circle areas
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Forgetting the half on triangle / trapezoid formulas
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Key takeaways

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Tracks your progress across lessons.

Checkpoint

10 questions on Area and Volume, from our question bank. Score 70% or better across 10 answers to reach Silver and pass this step.

Lesson v1 · generated 5/2/2026 · the floating tutor knows you're on this lesson — ask anything.