An artist uses a regular decagon to make a frame. If the side is 12 cm, what's the total border length?
120 cm
A decagon is a ten-sided polygon, and "regular" means all ten sides are of equal length.
The border of the frame is simply the boundary of this polygon, i.e. its perimeter.
For any regular polygon the perimeter is \(P = n\times s\), where \(n\) is the number of sides and \(s\) the length of one side.
Here \(n = 10\) and \(s = 12\) cm.
Substituting, \(P = 10\times 12\).
This evaluates to \(P = 120\) cm.
The key idea is that a regular polygon's perimeter is just its side length repeated once for every side.
The total border length of the frame is 120 cm.
Similar Questions
A parallelogram has adjacent sides of 18 cm and 10 cm, and the angle between them is 60°. Find the exact area of the parallelogram and the height corresponding to the longer side.
A circular embankment is constructed with a radius of 40 meters. A second concentric circular embankment is built around the first, with a width of 12 meters. What is the approximate area of the region between the two embankments?
A circular sprinkler is placed inside a triangular garden with sides 13 m, 14 m, and 15 m. What is the radius of the sprinkler if it touches all three sides of the triangle?
An interior designer uses a regular pentagon shape for a tabletop. What is the measure of each interior angle?
The ratio of the length and perimeter of a rectangle is 7:22, respectively. If the area of the rectangle is 1,792 cm², then find the breadth of the rectangle.
A conference hall of 6 m × 4 m is to be tiled using 60 cm × 40 cm tiles. How many are needed?
A circle is inscribed within a square with a side length of 18 cm. Find the area of the part of the square not covered by the circle.
A classroom wall of size 6 m x 3 m is to be covered using cuboid-shaped foam panels of size 2 m x 1 m x 0.1 m (thickness irrelevant). How many such panels are needed to cover the wall completely?
The ratio of the length to the width of a rectangle is 7:4. If its perimeter is 88 cm, what is its area?
A designer creates a regular polygonal clock with each internal angle 150°. How many sides does it have?
Important Questions from Plane Figures
If the area of a square is 625 cm 2, then what is the perimeter of the square?
The perimeter of a semi circle is 25.7 cm. What is its diameter (in cm)? (π = 3.14)
If the perimeter of an equilateral triangle is 48 cm, find its area:
The area of an isosceles right angled triangle is 121 cm 2. Find its hypotenuse.
- In Δ ABC, length of perpendicular from A to BC is 15 cm and BC = 8 cm and AC = 24 cm, then find the length of perpendicular from B to AC.
