Study on the flySHSATMathematicsArea, perimeter, volume, and surface area
Mathematics
Area measures the space inside a flat figure in square units, perimeter measures the distance around it, and volume and surface area extend those ideas to solid figures.
Mixing them up is the classic error, such as using the circumference formula when a question supplies the area of a circle. Problems on area, perimeter, volume, and surface area often work backward: a known area leads to the radius, which then gives the circumference, or a perimeter and a ratio of sides lead to the actual lengths.
Some questions use solids built from unit cubes and ask how many cubes lie hidden inside or touch the outside.
Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.
Question 1Mid
The side lengths of a rectangle are in the ratio . If the perimeter of the rectangle is 78, what is the area of the rectangle, in square units?
Answer: D — 360
The perimeter is . Since , . The side lengths are 15 and 24, so the area is .
Question 2Mid
A rectangular prism is built from unit cubes and has dimensions 4 units by 5 units by 6 units. How many of the unit cubes do not touch any outside face of the prism?
Answer: C — 24
Removing the outside layer from each dimension leaves an interior block measuring by by unit cubes. That is cubes that do not touch any outside face.
Question 3Mid
A circular window has an area of square inches. What is the circumference of the window in inches?
Answer: B —
From , the radius is 11 inches. Therefore, the circumference is inches.
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Practice 153 Area, perimeter, volume, and surface area questions in the app
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