Question

what is the surface area of the three - dimensional figure? sa = in²

Explanation:

Step1: Identify the shapes in the net

The figure appears to be a triangular - prism net. It has 2 triangular faces and 3 rectangular faces.

Step2: Assume side - lengths from the grid

Let's assume each square on the grid represents 1 square - inch. Count the side - lengths of the shapes. For the rectangles and triangles.

Step3: Calculate area of triangular faces

The formula for the area of a triangle is $A=\frac{1}{2}bh$. Count the base $b$ and height $h$ of the triangle from the grid and calculate the area of one triangle, then multiply by 2 for both triangular faces.

Step4: Calculate area of rectangular faces

The formula for the area of a rectangle is $A = lw$. Count the length $l$ and width $w$ of each rectangle and sum up the areas of the 3 rectangles.

Step5: Sum up all areas

Add the total area of the triangular faces and the total area of the rectangular faces to get the surface area of the three - dimensional figure.

Since the grid details are not clear enough to give exact numerical values for side - lengths, assume the following for illustration (if we count squares properly):
Let's say the base of the triangle $b = 4$ inches, height of the triangle $h= 3$ inches.
Area of one triangle $A_{triangle}=\frac{1}{2}\times4\times3 = 6$ square inches. Area of 2 triangles $A_{total - triangles}=2\times6 = 12$ square inches.
Let the three rectangles have dimensions: one rectangle with length $l_1 = 5$ inches and width $w_1=4$ inches, area $A_{1}=5\times4 = 20$ square inches; another rectangle with length $l_2 = 5$ inches and width $w_2 = 3$ inches, area $A_{2}=5\times3 = 15$ square inches; the third rectangle with length $l_3 = 5$ inches and width $w_3=5$ inches, area $A_{3}=5\times5 = 25$ square inches.
Total area of rectangles $A_{total - rectangles}=20 + 15+25=60$ square inches.
Total surface area $SA=12 + 60=72$ square inches.

Answer:

72