Before you read

Answer first — the lesson below explains it.

A contractor is tiling a rectangular kitchen floor that measures 15 inches by 8 inches per tile. What is the area covered by one tile?

A
46 in $^{2}$
B
92 in $^{2}$
C
120 in $^{2}$
D
240 in $^{2}$

Check your answer

Answer:

Before you read

Answer first — the lesson below explains it.

A landscaper is laying sod on a triangular patch of lawn with a base of 14 cm and a perpendicular height of 9 cm. What area of sod is needed?

A
63 cm $^{2}$
B
126 cm $^{2}$
C
56 cm $^{2}$
D
23 cm $^{2}$

Check your answer

Answer:

Theory

Area Formulas

Rectangle: $A = l \times w$

Square: $A = s^2$

Triangle: $A = \frac{1}{2}bh$ (where $b$ = base, $h$ = height perpendicular to base)

Triangle: A = ½bh

Right triangle with legs as base and height

Parallelogram: $A = bh$

Trapezoid: $A = \frac{1}{2}(b_1 + b_2)h$ (average of the two parallel sides $\times$ height)

Example 1

A triangle has a base of 10 cm and a height of 6 cm. What is its area?

$A = \frac{1}{2}(10)(6) = 30$ cm $^{2}$

30 cm

^{2}

Example 2

A trapezoid has parallel sides of 8 m and 12 m, and a height of 5 m. What is its area?

$A = \frac{1}{2}(8 + 12)(5) = \frac{1}{2}(20)(5) = 50$ m $^{2}$

50 m

^{2}

Quick check

You just read it. Can you apply it?

A flower bed is shaped like a trapezoid with parallel sides of 6 ft and 10 ft and a height of 4 ft. What area of mulch is needed to cover it?

A
24 ft $^{2}$
B
32 ft $^{2}$
C
40 ft $^{2}$
D
60 ft $^{2}$

Check your answer

Answer:

$A = \frac{1}{2} (6 + 10) (4) = \frac{1}{2} (16) (4) = 32$ ft $^{2}$ .

Common Mistakes

Common Mistakes to Avoid

Using slant height instead of perpendicular height

In triangles and parallelograms, the height MUST be perpendicular to the base.

Remember: avoid this error.

Forgetting the

\frac{1}{2}

in the triangle formula

$A = \frac{1}{2}bh$ , not $bh$ .

Remember: avoid this error.

Units

Area is always in square units (cm $^{2}$ , m $^{2}$ , ft $^{2}$ ).

Remember: avoid this error.

Quick check

You just read it. Can you apply it?

An interior designer has 24 cm of decorative trim to border either a square frame or a rectangular frame (length 8 cm). Both use all 24 cm. Which frame encloses more area?

A
The square (36 cm $^{2}$ )
B
The rectangle (32 cm $^{2}$ )
C
They have the same area
D
The rectangle (48 cm $^{2}$ )

Check your answer

Answer:

Square: side $= 24/4 = 6$ , area $= 36$ . Rectangle: width $= (24 - 16) /2 = 4$ , area $= 8 \times 4 = 32$ . The square encloses more area.

Strategy

SAT Pro Tip

The SAT provides a reference sheet with all area formulas. But knowing them by heart saves time. The most commonly tested: triangle ( $\frac{1}{2}bh$ ) and the relationship between a parallelogram and a triangle (a parallelogram is 2 triangles).

After reading

Same question as before. What do you say now?

A contractor is tiling a rectangular kitchen floor that measures 15 inches by 8 inches per tile. What is the area covered by one tile?

A
46 in $^{2}$
B
92 in $^{2}$
C
120 in $^{2}$
D
240 in $^{2}$

Check your answer

Answer:

$A = 15 \times 8 = 120$ in $^{2}$ .

After reading

Same question as before. What do you say now?

A landscaper is laying sod on a triangular patch of lawn with a base of 14 cm and a perpendicular height of 9 cm. What area of sod is needed?

A
63 cm $^{2}$
B
126 cm $^{2}$
C
56 cm $^{2}$
D
23 cm $^{2}$

Check your answer

Answer:

$A = \frac{1}{2} (14) (9) = 63$ cm $^{2}$ .

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