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
[tex]\text{Area of equilateral triangle = s}^2\times\frac{\sqrt[]{3}}{4}[/tex]
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)
