AREA OF COMPOUND SHAPES

Find the area of compound shapes given below.

Problem 1 :

Solution :

Area of Compound Shapes = Area of rectangle + area of trapezoid

Problem 2 :

Solution :

By drawing the horizontal line in the middle, we get two parallelograms of same measures.

Area of parallelogram = base x height

height of one parallelogram = 26

= 2(35× 26)

= 3640

So, area of the shape is 3640 cm²

Problem 3 :

Solution :

By drawing the horizontal line in the middle, we divide the original shape into rectangle and trapezoid.

Problem 4 :

Solution :

Area of the shape 

= area of semi circle + area of rectangle

= (1/2) πr² + (l × w)

= (1/2) π(2.05)² + (4.1 × 4.7)

= (1/2) π(4.2025) + 19.27

= 2.10125π +19.27

= 2.10125(3.14) +19.27

= 6.60 + 19.27

= 25.87 cm²

Problem 5 :

Solution :

Area of the shape = area of semi circle + area of triangle

= (1/2) πr² + (1/2) b × h

= (1/2) π(11)² + (1/2) x (22) × (16)

= (1/2) π(121) + 176

= π(60.5) + 176

= (3.14) × (60.5) + 176

= 189.97 + 176  

= 365.97 cm²

Problem 6 :

Solution :

Area of the shape

= 3(area of semi circle) + area of rectangle

= 3((1/2) πr²)) + (l × w)

= 1.5 x (3.14) × 4² + (8 × 8)

= 1.5 (3.14) × 16 + 64

= 75.36 + 64

= 139.36 cm²