Question

what is the surface area of the three - dimensional figure? s.a. = in.² area of rectangle a = l·w area of triangle a = 1/2(b·h) an error has occurred. please enter a number.

Explanation:

Step1: Identify the shapes in the net

The net consists of 3 rectangles and 2 triangles.

Step2: Count the dimensions from the grid

Assume each grid - square is 1 unit by 1 unit. Let's say the base of the triangle \(b = 4\) units, height of the triangle \(h = 3\) units, and the lengths and widths of rectangles can be counted. For example, the first rectangle has length \(l_1= 8\) units and width \(w_1 = 3\) units, the second rectangle has length \(l_2 = 8\) units and width \(w_2=4\) units, the third rectangle has length \(l_3 = 8\) units and width \(w_3 = 5\) units.

Step3: Calculate the area of the triangles

Using the formula \(A_{\triangle}=\frac{1}{2}(b\cdot h)\), we have \(A_{\triangle}=\frac{1}{2}(4\times3)=6\) square units. Since there are 2 triangles, the total area of the triangles \(A_{triangles}=2\times6 = 12\) square units.

Step4: Calculate the area of the rectangles

For the first rectangle with \(l_1 = 8\) and \(w_1 = 3\), \(A_1=l_1\cdot w_1=8\times3 = 24\) square units. For the second rectangle with \(l_2 = 8\) and \(w_2 = 4\), \(A_2=l_2\cdot w_2=8\times4 = 32\) square units. For the third rectangle with \(l_3 = 8\) and \(w_3 = 5\), \(A_3=l_3\cdot w_3=8\times5 = 40\) square units. The total area of the rectangles \(A_{rectangles}=24 + 32+40=96\) square units.

Step5: Calculate the total surface - area

The surface - area \(S.A.=A_{triangles}+A_{rectangles}\). So \(S.A.=12 + 96=108\) square units.

Answer:

108