Measurement & data
Perimeter, area, and volume
TEAS math
Perimeter walks the border, area covers the inside, volume fills the space.
What this covers
Arect=l⋅w,Atri=21bh,V=l⋅w⋅h- Decide which quantity the question is really asking for before touching numbers.
- Perimeter adds boundary lengths; repeated equal sides can be grouped with multiplication.
- For a rectangle, area is length times width; a triangle uses half its base times perpendicular height.
- A rectangular prism's volume multiplies its three perpendicular dimensions, giving cubic units.
Worked example
Worked example
A 12 ft by 5 ft room: how much trim for the border, and how much carpet for the floor?
- P=2(12+5)=34ftTrim runs along the border, so add the sides.
- A=12⋅5=60ft2Carpet covers the inside, so multiply the sides.
Another worked example
A rectangular box is 3 cm long, 4 cm wide, and 5 cm high. Find base area and volume.
- B=3⋅4=12 cm2Two perpendicular lengths cover the base.
- V=Bh=12⋅5=60 cm3The constant base extends through 5 cm of perpendicular height.
A common mistake
A mistake Lemma catches
From P=2(12+5)=34ft
A=2(12+5)A=12⋅5
“Carpet covers the floor, so it is an area in square feet: 12 · 5 = 60 ft². 2(12 + 5) = 34 ft is the distance around the room — the trim, not the carpet.”
Try one
Sample problem
A room measures 11 feet by 6 feet. How many square feet of flooring cover it? Enter the number.
A=11⋅6Practice geometry measures free
No account, no email. Every line you type is checked by the same computer algebra system as the worked example above.
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