Question

(a) find the following side lengths for the net.
a = mm
b = mm
c = mm
d = mm
(b) use the net to find the surface area of the prism.
mm²

Explanation:

Part (a)

Step1: Determine \(A\)

\(A\) is the same as the base of the rectangular part which is \(17\) mm.

Step2: Determine \(B\)

\(B\) is the height of the rectangular part which is \(3\) mm.

Step3: Determine \(C\)

\(C\) is the same as one of the sides of the triangular part which is \(8\) mm.

Step4: Determine \(D\)

\(D\) is the same as the other side of the triangular part which is \(15\) mm.

Part (b)

Step1: Calculate the area of the two triangular faces

The area of a triangle is \(A_{\text{triangle}}=\frac{1}{2}\times base\times height\). For the given right - triangle with base \(8\) and height \(15\), \(A_{\text{triangle}}=\frac{1}{2}\times8\times15 = 60\) \(mm^{2}\). The area of two triangular faces is \(2\times60=120\) \(mm^{2}\).

Step2: Calculate the area of the three rectangular faces

The three rectangles have dimensions:

• One with dimensions \(17\times3\), its area \(A_{1}=17\times3 = 51\) \(mm^{2}\)
• One with dimensions \(8\times3\), its area \(A_{2}=8\times3=24\) \(mm^{2}\)
• One with dimensions \(15\times3\), its area \(A_{3}=15\times3 = 45\) \(mm^{2}\)

The sum of the areas of the three rectangular faces is \(A_{r}=51 + 24+45=120\) \(mm^{2}\)

Step3: Calculate the total surface area

The total surface area \(A = A_{\text{triangles}}+A_{r}\). So \(A=120 + 120=240\) \(mm^{2}\)

Answer:

(a) \(A = 17\) mm, \(B = 3\) mm, \(C = 8\) mm, \(D = 15\) mm
(b) \(240\) \(mm^{2}\)