Question

a triangular prism and its net are shown below. the top and bottom of the prism are shaded. (all lengths are in centimeters.) (a) find the following side lengths for the net. a = \\(\square\\) cm b = \\(\square\\) cm c = \\(\square\\) cm d = \\(\square\\) cm (b) use the net to find the lateral surface area of the prism. neither the top nor bottom is included. \\(\square\\) \\(\text{cm}^2\\) (c) use the net to find the total surface area of the prism. \\(\square\\) \\(\text{cm}^2\\)

Explanation:

Step1: Match net sides to prism

• $A$ matches prism height: $A=7$
• $B$ matches prism edge: $B=15$
• $C$ matches prism edge: $C=8$
• $D$ matches prism edge: $D=17$

Step2: Calculate lateral surface area

Find sum of rectangular face areas:
$\text{Lateral Area} = (15 \times 7) + (8 \times 7) + (17 \times 7)$
$= 105 + 56 + 119 = 420$

Step3: Calculate triangular base area

Use right triangle area formula:
$\text{Area of 1 triangle} = \frac{1}{2} \times 8 \times 15 = 60$
Total area for 2 triangles: $2 \times 60 = 120$

Step4: Calculate total surface area

Add lateral and triangular areas:
$\text{Total Area} = 420 + 120 = 556$

Answer:

a) $A=7$ cm, $B=15$ cm, $C=8$ cm, $D=17$ cm
b) $420$ $\text{cm}^2$
c) $556$ $\text{cm}^2$