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Area and perimeterGeometryMiddle schoolabout 0:44

Find the area of a regular pentagon with side 4: animated lesson

A narrated, step-by-step area and perimeter video lesson with captions. Final answer: Area = 27.52763841 square units; perimeter = 20 units.

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Video with a synthetic English voice and captions. Pick another language for subtitles in that language, or open the interactive version.

Video narrated by a synthetic voice (Piper TTS, en_US-ljspeech-high voice (LJ Speech dataset, public domain)); the steps come from our maths engine and the answer was checked independently. Download MP4 (0.3 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Worked example
Find the area of a regular pentagon with side 4.
2. Step by step
1. $a = \frac{s}{2\tan(\pi/5)} \approx 2.752763841$
  Apothem (centre to the middle of a side)
2. $A = \frac{1}{2} \cdot 5 \cdot 4 \cdot 2.752763841 \approx 27.52763841$
  Half the perimeter times the apothem
3. The answer
$A = 27.52763841$
A = 27.52763841
4. Check
- The area 27.52763841 is positive and in square units.

Transcript

The problem. Here is the problem: Find the area of a regular pentagon with side 4. Compute the area from the shape prime s dimensions, all in the same length unit; the area is in that unit squared.

Step by step. Apothem (centre to the middle of a side). Half the perimeter times the apothem.

The answer. So the answer is Area equals 27.52763841 square units; perimeter equals 20 units. Area measures how many unit squares fit inside a flat shape, so it is always in squared units such as cm squared or m squared.

Check. The area 27.52763841 is positive and in square units.

About area and perimeter

Find the area and perimeter of rectangles, triangles, sectors and other plane shapes.

Find the area of a regular pentagon with side 4 (Lesson)