Question

Find the Lateral Surface Area of the triangular prism.The height 8.3 is not in the question but can you work one without 8.3Question 5 options:420 cm2462 cm2581 cm2503 cm2

Answer 1

Step-by-step explanation:

Lateral Surface Area of the triangular prism = (perimeter × height) + 2(area of base)

Since it is anequilateral triangle, all 3 sides of the triangle are equal

Perimeter = 10cm + 10cm + 10cm = 30 cm

area of base = area of triangle

`\text{Area of equilateral triangle = s}^2*\frac{\sqrt[]{3}}{4}`

Area of equilateral triangle = side² × (√3)/4

side = 10cm

Area of equilateral triangle = 10² × (√3)/4 = 100/4 × √3 = 25√3

height = 14cm

Lateral Surface Area of the triangular prism = (30 cm × 14cm) +2(25√3)

Lateral Surface Area of the triangular prism = 420 + 50√3 = 420 + 86.6

Lateral Surface Area of the triangular prism = 506.6cm²

The area of triangle used = 1/2 bh = 1/2(10cm)(8.3cm) = 83cm²

The Lateral Surface Area of the triangular prism = 420 + 83 = 503 cm² (4th option)