# AREA OF COMPOUND SHAPES RECTANGLES AND TRIANGLES

Two or more basic shapes put together is known as compound shapes.

Find the area of the following compound shapes (not drawn to scale)

The dashed lines are perpendicular.

Problem 1 :

Solution :

By observing the figure,

Area of a rectangle A = l × w

Length of a rectangle (l) = 4 cm

Width of a rectangle (w) = 9 cm

Area of a rectangle A = 4 × 9

= 36 cm2

Area of a triangle A = 1/2 (b × h)

Base of a triangle (b) = 5 cm

Height of a triangle (h) = 6 cm

= 1/2 (5 × 6)

= 1/2 (30)

= 15 cm2

Area of Compound Shapes = Area of a rectangle + Area of a triangle

= 36 + 15

= 51 cm2

Problem 2 :

Solution :

By observing the figure,

Area of a rectangle A = l × w

Length of a rectangle (l) = 3 cm

Width of a rectangle (w) = 6 cm

Area of a rectangle A = 3 × 6

= 18 cm2

Area of a triangle A = 1/2 (b × h)

Base of a triangle (b) = 3 cm

Height of a triangle (h) = 6 cm

= 1/2 (3 × 6)

= 1/2 (18)

= 9 cm2

Area of Compound Shapes = Area of a rectangle + Area of a triangle

= 18 + 9

= 27 cm2

Problem 3 :

Solution :

By observing the figure,

Area of a rectangle A = l × w

Length of a rectangle (l) = 8 cm

Width of a rectangle (w) = 6 cm

Area of a rectangle A = 8 × 6

= 48 cm2

Area of a triangle A = 1/2 (b × h)

Base of a triangle (b) = 1 cm

Height of a triangle (h) = 6 cm

= 1/2 (1 × 6)

= 1/2 (6)

= 3 cm2

Area of a triangle A = 1/2 (b × h)

Base of a triangle (b) = 8 cm

Height of a triangle (h) = 3 cm

= 1/2 (8 × 3)

= 1/2 (24)

= 12 cm2

Area of Compound Shapes = Area of a rectangle + Area of a triangle + Area of a triangle

= 48+ 3 + 12

= 63 cm2

Problem 4 :

Solution :

By observing the figure,

Area of a rectangle A = l × w

Length of a rectangle (l) = 4 cm

Width of a rectangle (w) = 4 cm

Area of a rectangle A = 4 × 4

= 16 cm2

Area of a triangle A = 1/2 (b × h)

Base of a triangle (b) = 4 cm

Height of a triangle (h) = 4 cm

= 1/2 (4 × 4)

= 1/2 (16)

= 8 cm2

Area of Compound Shapes = Area of a rectangle + Area of a triangle

= 16 + 8

= 24 cm2

Problem 5 :

Solution :

By observing the figure,

Area of a rectangle A = l × w

Length of a rectangle (l) = 10 cm

Width of a rectangle (w) = 4 cm

Area of a rectangle A = 10 × 4

= 40 cm2

Area of a triangle A = 1/2 (b × h)

Base of a triangle (b) = 10 cm

Height of a triangle (h) = 3 cm

= 1/2 (10 × 3)

= 1/2 (30)

= 15 cm2

Area of a triangle A = 1/2 (b × h)

Base of a triangle (b) = 10 cm

Height of a triangle (h) = 4 cm

= 1/2 (10 × 4)

= 1/2 (40)

= 20 cm2

Area of Compound Shapes = Area of a rectangle + Area of a triangle + Area of a triangle

= 40 + 15 + 20

= 75 cm2

Problem 6 :

Solution :

By observing the figure,

Area of a rectangle A = l × w

Length of a rectangle (l) = 10 cm

Width of a rectangle (w) = 4 cm

Area of a rectangle A = 10 × 4

= 40 cm2

Area of a triangle A = 1/2 (b × h)

Base of a triangle (b) = 7 cm

Height of a triangle (h) = 6 cm

= 1/2 (7 × 6)

= 1/2 (42)

= 21 cm2

Area of Compound Shapes = Area of a rectangle + Area of a triangle

= 40 + 21

= 61 cm2

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