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1 1
• Area of triangle BDF = of area of rectangle ABCD + of area of rectangle BEFC = ...............
2 2
area of rectangle AEFD.
• Also, area of triangle ADF = ............... of area of rectangle AEFD.

Conclusion: The area of a triangle lying on the same base and having the same height that of a
1
rectangle = of the area of the rectangle.
2
Example 15: Find the areas of the figures below by dividing them into rectangles and triangles.

(a) (b)

Solution: (a) We can divide the given figure into rectangles and triangles as shown here.
Area of figure AHCEF = Area of triangle AGH + Area of triangle CDH A B C

+ Area of rectangle GDEF G O D
1 1 H
Area of triangle AGH = × Area of rectangle ABHG = × (2 × 1) = 1 sq. unit
2 2
1 1 F E
Area of triangle CDH = × Area of rectangle BCDH = × (3 × 2) = 3 sq. units
2 2

Area of rectangle GDEF = (4 × 3) = 12 sq. units
So, area of figure AHCEF = 1 sq. unit + 3 sq. units + 12 sq. units = 16 sq. units.

Alternative way:
1
Area of figure AHCEF = Area of rectangle ACEF – Area of triangle AHC (= area of rectangle ACDG)
2
1
= (4 × 5) sq. units – × (4 × 2) sq. units = 20 sq. units – 4 sq. units
2
= 16 sq. units

(b) We can divide the given figure into squares and triangles as shown alongside. A B C

Area of figure BDFH = Area of triangle BDH + Area of triangle FDH
H D D
1 1
Area of triangle BDH = × Area of rectangle ACDH = × (4 × 2) = 4 sq. units
2 2
1 1 E
Area of triangle FDH = × Area of square DEGH = × (4 × 4) = 8 sq. units G F
2 2
So, area of figure BDFH = 4 sq. units + 8 sq. units = 12 sq. units.

Teacher’s Explain the students that every square is a rectangle.
Tip

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