Question

find the surface area:

Explanation:

Step1: Identify the shapes

The figure consists of 2 congruent triangles and 3 rectangles.

Step2: Calculate area of triangles

The area formula for a triangle is $A_{triangle}=\frac{1}{2}\times base\times height$. Here, base = 8 cm and height = 3 cm. So $A_{triangle}=\frac{1}{2}\times8\times3 = 12$ $cm^{2}$. The total area of 2 triangles is $2\times12=24$ $cm^{2}$.

Step3: Calculate area of first rectangle

One rectangle has dimensions 10 cm and 8 cm. Its area $A_{1}=10\times8 = 80$ $cm^{2}$.

Step4: Calculate area of second rectangle

Another rectangle has dimensions 10 cm and 5 cm. Its area $A_{2}=10\times5 = 50$ $cm^{2}$.

Step5: Calculate area of third rectangle

The third rectangle has dimensions 10 cm and the length of the hypotenuse of the triangle. Using the Pythagorean theorem for the triangle with legs 3 cm and 8 cm, the hypotenuse $l=\sqrt{3^{2}+8^{2}}=\sqrt{9 + 64}=\sqrt{73}\approx 8.54$ cm. Its area $A_{3}=10\times\sqrt{73}\approx85.4$ $cm^{2}$.

Step6: Calculate total surface - area

The total surface area $A = 24+80 + 50+85.4=239.4$ $cm^{2}$.

Answer:

$239.4$ $cm^{2}$