Answer:
Explanation:
To find the surface area of the solid given the net, we need to identify all of the faces and add up their areas. Looking at the net, we can see that the solid consists of a rectangular prism and two triangular prisms attached to its sides.
To find the area of the rectangular prism, we need to multiply the length, width, and height. From the net, we can see that the length is 12 units, the width is 5 units, and the height is 8 units. So, the area of the rectangular prism is:
Area = length * width * height
Area = 12 units * 5 units * 8 units
Area = 480 units²
To find the area of the triangular prisms, we need to multiply the base, height, and half the width. From the net, we can see that the base of each triangular prism is 12 units and the height is 8 units. To find the width, we can use the Pythagorean theorem:
width² = height² + base²/4
width² = 8² + 12²/4
width² = 64 + 36
width² = 100
width = 10 units
So, the area of each triangular prism is:
Area = 1/2 * base * height * width
Area = 1/2 * 12 units * 8 units * 10 units
Area = 480 units²
Now, we can add up the areas of all three faces to find the total surface area:
Surface area = area of rectangular prism + area of two triangular prisms
Surface area = 480 units² + 480 units² + 480 units²
Surface area = 1440 units²
Therefore, the surface area of the solid given the net is 1440 units². None of the answer choices match exactly, but the closest one is A. 1292 units².