Question

Find the surface area of the solid formed by the net. Round your answer to the nearest hundredth.

Answer 1

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

$A_{rectangle}=b\times h=20 \times 8 =160 cm^{2}$

The area of all rectangles is

$A_{rectangles}=3(160cm^{2})=480 cm^{2}$, because there are three rectangles in total.

The area of each triangle is

$A_{triangle }=\frac{\sqrt{3} }{4} (8cm)^{2} =\frac{\sqrt{3} }{4}(64cm^{2} )\\A_{triangle }=16\sqrt{3} cm^{2}$

The area of both triangles is

$A_{triangles}=2(16\sqrt{3}cm^{2} )=32\sqrt{3} cm ^{2}$

Now, the area of the whole figure is the sum of the area of triangles and rectangles

$A_{total}=480cm^{2} +32\sqrt{3} cm^{2} \approx 535.43 cm^{2}$

Therefore, the area of the total figure is around 535.43 square centimeters.