Perimeter and Area of Rectangles and Triangles

What you’ll learn

Distinguish boundary length from covered surface.

បែងចែកបរិមាត្រ និងផ្ទៃក្រឡា។

Meaning and use

Perimeter is the total boundary length; area measures the covered two-dimensional surface. A triangle uses a perpendicular height, not automatically the sloping side. Convert all lengths to a common unit before calculating. Linear units and square units describe different quantities.

បរិមាត្រជាប្រវែងជុំវិញ ហើយផ្ទៃក្រឡាជារង្វាស់ផ្ទៃ។ កម្ពស់ត្រីកោណត្រូវកែងនឹងបាត មិនមែនជ្រុងទ្រេតជានិច្ចទេ។

Formulas

Rectangle

\[P=2(l+w),\qquad A=lw\]

Triangle

\[A=\frac12 bh\]

Symbols and units

Symbol	Meaning	Unit or restriction
P	Perimeter	cm, m, or another length unit
A	Area	cm², m², or another square unit
l, w	Rectangle length and width	Same length unit
b, h	Triangle base and perpendicular height	Same length unit

Conditions and limits

• Rectangle formulas require a rectangle, with four right angles.
• Triangle height must be perpendicular to the selected base.
• ប្រើឯកតាប្រវែងដូចគ្នា ហើយសរសេរផ្ទៃក្រឡាជាឯកតាការ៉េ។

Worked examples

A rectangle

A rectangle is 8 cm long and 3 cm wide.

1. Perimeter \(P=2(8+3)=22\) cm.
2. Area \(A=8\times3=24\) cm².

P = 22 cm; A = 24 cm²

បរិមាត្របូកជ្រុងទាំងអស់ ខណៈផ្ទៃក្រឡាគុណបណ្ដោយនិងទទឹង។

A triangle

Base is 10 m and perpendicular height is 6 m.

1. Use \(A=\frac12 bh\).
2. Calculate \(A=\frac12\times10\times6=30\) m².

30 m²

ត្រូវយកពាក់កណ្ដាលផលគុណបាតនិងកម្ពស់។

Common mistakes

Instead of	Use	Why
Area = 2(l + w).	Area = lw.	2(l + w) gives the rectangle’s perimeter.
A triangle with base 10 m and height 6 m has area 60 m².	Its area is 30 m².	The triangle formula includes one half.

Practice

Solve these before revealing the worked solutions. Include units where relevant.

សាកល្បងដោះស្រាយមុនបើកមើលចម្លើយ។ សូមបង្ហាញជំហាន និងឯកតាដែលពាក់ព័ន្ធ។

1. Find the perimeter of a 5 cm by 4 cm rectangle.
2. Find its area.
3. A triangle has base 12 cm and height 5 cm. Find its area.

Answers and steps

Show solutions / បង្ហាញដំណោះស្រាយ

1. 18 cm

   2(5 + 4) = 18.

2. 20 cm²

   5 × 4 = 20; area has square units.

3. 30 cm²

   One half × 12 × 5 = 30.

Quick recap

• Perimeter and area answer different questions.
• Use perpendicular triangle height.
• Check units before and after calculation.