Answer B
Step-by-step explanation:
You need to first find the surface area of the triangular prism.
In order to do that, we need to first know the length of the base of the triangles on both side. So, I used the pythagorean theorem (a²+b²=c²) after making the triangle a right triangle by cutting it in HALF.
a²+b²=c²
a²+2.6²=3²
a²+6.76=9
Subtract 6.76 on both sides
a²=2.24
a=√2.24
a=1.49666295471
Now, we know that the base of HALF of the triangles on both sides of the prism is 1.496
We need to MULTIPLY this by 2 to get the full length. So, the length of the bases of both triangles is 2.99332590942
The height of the triangles is 2.6
We are going to first find the area of one triangle and multiply it by 2, to get the area of both triangles.
Area of a triangle = base x height ÷ 2
2.6 x 2.99332590942= 7.78264736449
7.78264736449 ÷ 2 = 3.89132368224
3.89132368224 x 2 (because we have 2 triangles) =7.78264736449 Â cm squared
Now, we know the area of both triangles, but we now need to add the add the surface area of the rectangles in the net.
Area of a rectangle = length x width
We know that all of the three rectangles are equal in size, and that the length of each one of them is 15 cm. However, the width/height of each one is unknown. We will find out the height of each one by looking at the length of the base of the triangle attached to the first one. We know that because of the base of the triangles = 2.99332590942, the width of the attached rectangles are 2.99332590942. We found this using the Pythagorean theroem (look above).
15 x 2.99332590942= 44.8998886413
44.8998886413 x 3 (because we have 3 of the same rectangles)= 134.699665924 cm squared
Now, we must ADD the surface area of the rectangles AND the triangles.
7.78264736449 (triangles) + 134.699665924 (the three rectangles)= 142.482313288 cm squared.
The CLOSEST OPTION to the answer we got is ANSWER B because it is 142.8 cm squared, which is the closest to the answer we got which was 142.482313288 cm squared.
I really hope this helps :)
