Answer:
The area of the total figure is around 535.43 square centimeters.
Step-by-step explanation:
In the image attached, you can notice that all rectangles have a base of 20 centimeters.
Also, each side of the equilaterals triangles is 8 centimeters.
Notice that the height of each rectangle is equal to a side of a triangle.
Using all given vales, the area of each rectangle is
[tex]A_{rectangle}=b\times h=20 \times 8 =160 cm^{2}[/tex]
The area of all rectangles is
[tex]A_{rectangles}=3(160cm^{2})=480 cm^{2}[/tex], because there are three rectangles in total.
The area of each triangle is
[tex]A_{triangle }=\frac{\sqrt{3} }{4} (8cm)^{2} =\frac{\sqrt{3} }{4}(64cm^{2} )\\A_{triangle }=16\sqrt{3} cm^{2}[/tex]
The area of both triangles is
[tex]A_{triangles}=2(16\sqrt{3}cm^{2} )=32\sqrt{3} cm ^{2}[/tex]
Now, the area of the whole figure is the sum of the area of triangles and rectangles
[tex]A_{total}=480cm^{2} +32\sqrt{3} cm^{2} \approx 535.43 cm^{2}[/tex]
Therefore, the area of the total figure is around 535.43 square centimeters.
