Frequently Asked Questions
What is perimeter?
Perimeter is the total boundary of a two-dimensional shape. It includes both the outer boundary and any inner boundaries (like the edges of holes inside the shape).
How do you calculate the perimeter of a rectangle?
The perimeter of a rectangle is the sum of all its four sides: P = 2w + 2h or P = 2(w + h), where w is the width and h is the height.
Why is a square's perimeter formula P = 4s?
A square is a special case of a rectangle where width and height are equal (w = h = s). Substituting this into the rectangle formula gives P = 2(s + s) = 4s.
How does a hole affect the perimeter?
Since perimeter measures the entire boundary of a shape, a hole adds to the perimeter. The total perimeter is the outer perimeter plus the inner perimeter (the perimeter of the hole).
How do you find the perimeter of a right-angled triangle if one side is missing?
Since we've already learned the Pythagorean theorem (a² + b² = c²), we can calculate the missing side length first and then sum all three sides together to get the perimeter.
What unit is used for perimeter?
Since perimeter is a one-dimensional length (boundary), it is measured in linear units like meters (m), centimeters (cm), feet (ft), or inches (in). It is never measured in square units, which are reserved for area.
How does doubling a shape's dimensions affect its perimeter and area?
Doubling all dimensions (scale factor of 2) doubles the perimeter (ratio 2:1) because perimeter is linear (1D). However, it quadruples the area (ratio 4:1) because area is two-dimensional (2D) and scales quadratically (2² = 4).
How does a caliper achieve 0.1 mm precision?
By matching a main scale (1 mm divisions) with a sliding Vernier scale (10 divisions spanning 9 mm, so each is 0.9 mm). The 0.1 mm difference accumulates: a 0.1 mm shift aligns the 1st Vernier mark, a 0.2 mm shift aligns the 2nd, and so on.
Why are rectangle diagonals equal?
Because by the Pythagorean theorem, right triangles with equal legs must have equal hypotenuses, meaning the diagonals are equal in length.