≡Mathematics EN 9th grade: Areas of Plane Figures
1. Square
A figure with 4 equal sides and right angles.
📌 Area formula:
\( A = l^2 \)
📌 Example:
If \( l = 5 \):
\( A = 5^2 = 25 \)
2. Rectangle
A figure with opposite sides equal and angles of \( 90^\circ \).
📌 Formula:
\( A = b \cdot h \)
📌 Example:
If \( b = 4 \) and \( h = 6 \):
\( A = 4 \cdot 6 = 24 \)
3. Parallelogram
A figure with opposite sides parallel.
📌 Formula:
\( A = b \cdot h \)
📌 Example:
\( b = 8 \) and \( h = 3 \):
\( A = 8 \cdot 3 = 24 \)
4. Triangle
📌 Formula:
\( A = \frac{b \cdot h}{2} \)
📌 Example:
\( b = 10 \) and \( h = 4 \):
\( A = \frac{10 \cdot 4}{2} = 20 \)
5. Regular polygon
All sides and angles are equal.
📌 Formula:
\( A = \frac{P \cdot a}{2} \)
Where:
\( P \) = perimeter
\( a \) = apothem
6. Trapezoid
Has two parallel bases.
📌 Formula:
\( A = \frac{(B + b)\cdot h}{2} \)
📌 Example:
\( B = 10, b = 6, h = 4 \)
\( A = \frac{(10 + 6)\cdot 4}{2} = 32 \)
7. Rhombus
📌 Formula:
\( A = \frac{D \cdot d}{2} \)
Where:
\( D \) = major diagonal
\( d \) = minor diagonal
📌 Example:
\( D = 8, d = 6 \)
\( A = \frac{8 \cdot 6}{2} = 24 \)
8. Kite (deltoid)
📌 Formula:
\( A = \frac{D \cdot d}{2} \)
✔ Same formula as the rhombus
9. Circle
📌 Formula:
\( A = \pi r^2 \)
📌 Example:
If \( r = 3 \):
\( A = \pi \cdot 3^2 = 9\pi \)
10. Important interpretation
✔ Figures with base and height → \( A = b \cdot h \)
✔ Triangle is half of a parallelogram
✔ Figures with diagonals → \( \frac{D \cdot d}{2} \)
✔ Circle uses \( \pi \)#
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