Question

The triangular prism shown has triangular _____face(s) and lateral face(s).

Answer 1

Answer:

The triangular prism shown has 2 triangular face(s) and 3 lateral face(s).

The area of one triangular face is 7.5 mm²

The surface area of the triangular prism is 135 mm²

Step-by-step explanation:

A triangular face of the prism is the face that has a three sided figure while the lateral faces are faces with four-sided figure. As seen from the triangular prism, it has 2 triangular faces since it is made up of 2 right angled triangles and has 3 lateral faces since it is made up of 3 rectangles which are 4 sided each.

Area of one triangular face = $\frac{1}{2} * base * height$

Given base = 2.5 mm and height = 6 mm

Area of one triangular face = $\frac{1}{2} *2.5 * 6$

$= 3*2.5\\= 7.5mm^{2}$

Surface area of triangular prism = bh + pH

b= base of the triangle  = 2.5 mm

h- height of the triangle  = 6 mm

p= perimeter of the triangle  = base + height + slant height = 2.5+6+6.5

p = 15 mm

H= height of the prism = 8mm

Surface area of triangular prism = 2.5(6)+15(8)

Surface area of triangular prism = 15 + 120

Surface area of triangular prism = 135mm²