Question

what is the surface area? 8 m 10 m 12 m 10 m 10 m square meters

Explanation:

Step1: Calculate area of triangular face

The area of a triangle is $A_{triangle}=\frac{1}{2}\times base\times height$. Here, base = 12 m and height = 8 m. So $A_{triangle}=\frac{1}{2}\times12\times8 = 48$ square - meters. There are 2 such triangular faces, so total area of triangular faces is $2\times48 = 96$ square - meters.

Step2: Calculate area of rectangular faces

There are 3 rectangular faces. Two have dimensions 10 m by 10 m and one has dimensions 12 m by 10 m.
The area of a rectangle is $A = length\times width$.
For the two 10 m by 10 m rectangles, their combined area is $2\times(10\times10)=200$ square - meters.
For the 12 m by 10 m rectangle, its area is $12\times10 = 120$ square - meters.
The total area of rectangular faces is $200 + 120=320$ square - meters.

Step3: Calculate total surface area

The total surface area of the solid is the sum of the area of triangular faces and rectangular faces. So $A_{total}=96 + 320=416$ square - meters.

Answer:

416