Question

80+ POINTS AND BRAINLIEST, EXPLANATION NEEDED! What is the surface area of the prism?

Answer 1

Answer:

$A = 234mm^{2}$

Step-by-step explanation:

A rectangular prism (or orthohedron) is a polyhedron whose surface is formed by two equal and parallel rectangles called bases and by four lateral faces that are also parallel rectangles and equal two to two.

The orthohedron is a straight prism and also a particular case of irregular quadrangular prism.

In a rectangular prism you can differentiate the following elements:

Bases: are two parallel and equal rectangles.

Faces: the four rectangles of the lateral faces and the two bases. Therefore, it has six faces.

Height : distance between the two bases of the prism. The height h coincides with any of the edges of the lateral faces.

Vertices: the eight points where three faces of the prism converge.

Edges: segments where two faces of the prism are found.

The surface area of ​​the rectangular prism (or orthohedron) is calculated by the following formula:

$A=2(wh+lw+lh)$ where w is width, l is length, and h is height.

Solving with l = 15mm, w = 3mm, and h = 4mm

$A=2[(3mm)(4mm)+(15mm)(3mm)+(15mm)(4mm)]$

$A=2(12mm^{2}+45mm^{2} +60mm^{2}) \\A=2(117mm^{2})\\A= 234mm^{2}$

Answer 2

Answer:

S.A. = 234mm²

Step-by-step explanation:

Look at the net of the prism in the picture.

We have

two rectangles 4mm × 15mm

two rectangles 3mm × 15mm

two rectangles 3mm × 4mm

The formula of an area of a rectangle: A = lw

l - length

w - width

l × w

Calculate the areas:

A₁ = 4mm · 15mm = 60mm²

A₂ = 3mm · 15mm = 45mm²

A₃ = 3mm · 4mm = 12mm²

The surface area:

S.A. = 2A₁ + 2A₂ + 2A₃

Substitute:

S.A. = 2 · 60 + 2 · 45 + 2 · 12 = 120 + 90 + 24 = 234mm²