Question

34 in.

Answer 1

Answer:

Step-by-step explanation:

Lateral surface area of the triangular prism = Perimeter of the triangular base × Height

By applying Pythagoras theorem in ΔABC,

AC² = AB² + BC²

(34)² = (16)² + BC²

BC = $\sqrt{1156-256}$

     = $\sqrt{900}$

     = 30 in.

Perimeter of the triangular base = AB + BC + AC

                                                      = 16 + 30 + 34

                                                      = 80 in

Lateral surface area = 80 × 22

                                  = 1760 in²

Total Surface area = Lateral surface area + 2(Surface area of the triangular base)

Surface area of the triangular base = $\frac{1}{2}(\text{Base})(\text{Height})$

                                                           = $\frac{1}{2}(30)(16)$

                                                           = 240 in²

Total surface area = 1760 + 2(240)

                               = 1760 + 480

                               = 2240 in²

Volume = Area of the triangular base × Height

             = 240 × 20

             = 4800 in³