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 cm^{2}
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 cm^{2}
Area of Compound Shapes = Area of a rectangle + Area of a triangle
= 36 + 15
= 51 cm^{2}
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 cm^{2}
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 cm^{2}
Area of Compound Shapes = Area of a rectangle + Area of a triangle
= 18 + 9
= 27 cm^{2}
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 cm^{2}
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 cm^{2}
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 cm^{2}
Area of Compound Shapes = Area of a rectangle + Area of a triangle + Area of a triangle
= 48+ 3 + 12
= 63 cm^{2}
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 cm^{2}
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 cm^{2}
Area of Compound Shapes = Area of a rectangle + Area of a triangle
= 16 + 8
= 24 cm^{2}
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 cm^{2}
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 cm^{2}
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 cm^{2}
Area of Compound Shapes = Area of a rectangle + Area of a triangle + Area of a triangle
= 40 + 15 + 20
= 75 cm^{2}
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 cm^{2}
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 cm^{2}
Area of Compound Shapes = Area of a rectangle + Area of a triangle
= 40 + 21
= 61 cm^{2}
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM