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Find the area of the combined shapes below.

a) A shape composed of a rectangle with dimensions 24cm x 24cm and a rectangle with dimensions 6cm x 10cm.

b) A shape composed of a trapezoid with the following dimensions: top side 12cm, bottom side 15cm, height 15cm.

c) A shape composed of a rectangle with dimensions 24cm x 18cm and a triangle with base 8cm and height 8cm.

d) A shape composed of a trapezoid with the following dimensions: top side 12cm, bottom side 8cm, height 11cm.

e) A shape composed of a trapezoid with the following dimensions: top side 10cm, bottom side 20cm, height 8cm.

f) A shape composed of a rectangle with dimensions 14cm x 13cm and a triangle with base 10cm and height 10cm.

Answer :

To find the area of combined shapes, we need to calculate the area of each individual shape in the combination and then sum them up.

a) Combined shape with two rectangles:

  • First rectangle: Length = 24 cm, Width = 24 cm. Area = $24 \times 24 = 576$ cm².
  • Second rectangle: Length = 6 cm, Width = 10 cm. Area = $6 \times 10 = 60$ cm².
  • Combined area = $576 + 60 = 636$ cm².

b) Trapezoid:

  • Top side = 12 cm, Bottom side = 15 cm, Height = 15 cm.
  • Area = [tex]\frac{1}{2} \times (\text{Top side} + \text{Bottom side}) \times \text{Height} = \frac{1}{2} \times (12 + 15) \times 15[/tex] cm².
  • Area = [tex]\frac{1}{2} \times 27 \times 15 = 202.5[/tex] cm².

c) Combined shape with a rectangle and a triangle:

  • Rectangle: Length = 24 cm, Width = 18 cm. Area = $24 \times 18 = 432$ cm².
  • Triangle: Base = 8 cm, Height = 8 cm. Area = [tex]\frac{1}{2} \times 8 \times 8 = 32[/tex] cm².
  • Combined area = $432 + 32 = 464$ cm².

d) Trapezoid:

  • Top side = 12 cm, Bottom side = 8 cm, Height = 11 cm.
  • Area = [tex]\frac{1}{2} \times (\text{Top side} + \text{Bottom side}) \times \text{Height} = \frac{1}{2} \times (12 + 8) \times 11[/tex] cm².
  • Area = [tex]\frac{1}{2} \times 20 \times 11 = 110[/tex] cm².

e) Trapezoid:

  • Top side = 10 cm, Bottom side = 20 cm, Height = 8 cm.
  • Area = [tex]\frac{1}{2} \times (\text{Top side} + \text{Bottom side}) \times \text{Height} = \frac{1}{2} \times (10 + 20) \times 8[/tex] cm².
  • Area = [tex]\frac{1}{2} \times 30 \times 8 = 120[/tex] cm².

f) Combined shape with a rectangle and a triangle:

  • Rectangle: Length = 14 cm, Width = 13 cm. Area = $14 \times 13 = 182$ cm².
  • Triangle: Base = 10 cm, Height = 10 cm. Area = [tex]\frac{1}{2} \times 10 \times 10 = 50[/tex] cm².
  • Combined area = $182 + 50 = 232$ cm².

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Rewritten by : Barada