Question

What is the area of the composite figure?

Answer 1

Answer:

The area of the composite figure is $A_{total} = 264(cm)^{2}$

Step-by-step explanation:

To find the area of this composite figure you need to follow this steps:

1. Separate the figure into simpler shapes whose area can be found.

        1.1 The first figure is a square with side 10 cm. So the area is $A=(10 cm)^{2}=100(cm)^{2}$

        1.2 The second figure is a triangle with a base 6 cm and a height 4 cm. So the area is $A=\frac{b*h}{2}=\frac{1*6*4}{2} =12(cm)^{2}$

        1.3 The third figure is a rectangle with length 8 cm and width 4 cm. So the area is $A = l*w=8cm*4cm=32(cm)^{2}$

        1.4 The fourth figure is a rectangle with length 20 cm and width 6 cm. So the area is $A = l*w=20cm*6cm=120(cm)^{2}$      

    2. Then add the areas together.

$A_{total} = A_{square} +A_{triangle}+A_{rectangle} +A_{rectangle}$

$A_{total} = 100(cm)^{2}+12(cm)^{2}+32(cm)^{2} +120(cm)^{2}$

$A_{total} = 264(cm)^{2}$

In the following image shows how we can separate the figure into simpler shapes.

Answer 2

Divide the figure into 3 shapes
top square
middle trapezoid
bottom rectangle

so
Area of figure 
= (10x10) + 1/2(8 + 14)(4) + (20 x 6)
= 100 + 44 + 120
= 264

answer
264 cm^2