EQN-04-02

Area & Perimeter

The area and perimeter formulas for the shapes the GAT-E actually uses — plus the circle facts.

~6 min read•Difficulty 2/5

Core formulas

Rectangle : area = length \times width perimeter = 2 (l + w)

Square : area = s^{2} perimeter = 4 s

Triangle : area = \frac{1}{2} \times base \times height

Parallelogram : area = base \times height

Trapezoid : area = \frac{1}{2} (b_{1} + b_{2}) \times height

Circles

circumference = 2 π r = π d

area = π r^{2}

On the GAT-E, leave answers in terms of $π$ unless told otherwise; the choices usually do.

Height must be perpendicular

In triangle and parallelogram area, the "height" is the perpendicular distance to the base — not a slanted side. Watch for figures that give you the slant and expect you to know the difference.

Composite shapes

Break an odd shape into rectangles, triangles, and circle parts; add or subtract their areas. A "shaded region" is almost always (big shape $-$ small shape).

Diagram

Area $=$ length $\times$ width; perimeter $= 2 \times ($ length $+$ width).

Worked examples

Example 1 (difficulty 1/5)

A rectangle has length 9 and width 4. What is its perimeter?

◎ Predict the answer first:

Example 2 (difficulty 1/5)

A circle has radius 5. What is its area? (Leave in terms of

π .)

◎ Predict the answer first:

Tips

Keep area (squared units) and perimeter/circumference (linear units) clearly separate.
For shaded regions, set up "outer area $-$ inner area" before computing anything.
$π r^{2}$ vs $2 π r :$ area has the square. If you see a wrong " $10 π$ " for radius 5, it confused the two.

Common mistakes

Using a slanted side as the height in triangle/parallelogram area

Why: The slant is the visible, labelled length.

Fix: Area uses the perpendicular height to the chosen base.

Mixing up area

π r^{2}

and circumference

2 π r

Why: Both formulas share

π

and r.

Fix: Area is the only one with r squared.

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