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 = 7 cm b = 8 cm c = 15 cm d = 17 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: Confirm part (a) values

Match prism sides to net labels.

Step2: Calculate lateral surface area

Sum areas of 3 rectangles:
$\text{Area}_1 = 7 \times 17 = 119$
$\text{Area}_2 = 8 \times 17 = 136$
$\text{Area}_3 = 15 \times 17 = 255$
$\text{Lateral Area} = 119 + 136 + 255 = 476$

Step3: Calculate triangle area

Use right triangle area formula:
$\text{Area}_{\text{triangle}} = \frac{1}{2} \times 8 \times 15 = 60$

Step4: Calculate total surface area

Add lateral area + 2×triangle area:
$\text{Total Area} = 476 + 2 \times 60 = 596$

Answer:

(a) $A=7$ cm, $B=8$ cm, $C=15$ cm, $D=17$ cm
(b) $476$ $\text{cm}^2$
(c) $596$ $\text{cm}^2$