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What is the surface area of the composite solid? A rectangular prism has a length of 15 meters, width of 10 meters, and height of 25 meters. A triangular prism has a triangular base with a base of 6 meters and height of 8 meters. The prism has a height of 15 meters. 1,508 m2 1,658 m2 1,808 m2 1,958 m2

Sagot :

buchinnamani208

Answer:

Surface area of rectangular prism = 1550m²

Surface area of triangular prism = 498m²

Step-by-step explanation:

The surface area of a rectangular prism is given by the formula

A= 2(wl+hl+hw)

Where A = surface area

w= width

l= length

h=height

Given that the rectangular prism has a length of 15 meters, width of 10 meters, and height of 25 meters.

A= 2(10×15+25×15+25×10)

A=2(150+375+250)

A=2(775)

A=1550 square meters

Surface area of triangular prism = base of triangle x height of triangle + (length of rectangle x width of rectangle) x 3

Since we are not given length and width of the triangular prism, we could assume the triangular prism has same length and width with the rectangular prism given that it is a composite shape(more than one solid in one)

Given triangular base with a base of 6 meters and height of 8 meters.

Surface area of triangular prism= 6×8+(10×15)×3

=48+150×3

=48+450

= 498 square meters

Surface area of a solid is the 2 dimensional space its surface covers. The surface area of the considered composite solid is given by: Option B: 1658 sq. meters

How to find the surface area of a composite figure?

Composite figure is figure made by composing two or more figure. The composite figure may leave a surface common as not a surface of the resultant composite figure due to it being the joining area of two figures, thus, not remaining a surface.

Thus, its surface area would sum of their surface areas - areas of those regions which are not surface anymore.

For the given case, the prisms given are having surface areas as:

Composite figure's surface area = Surface area of its composing figures - any overlapping areas

Surface area of rectangular prism  = [tex]2(L.W + W.H + H.L) = 2(15 \times 10 + 10 \times 25 + 25 \times 15) = 1550[/tex] sq. meters.

Surface area of triangular prism = area of its three rectangular faces + area of its base triangles.

For the triangle ABI, Pythagoras theorem is proved to be true with angle I (internally) being right angled triangle. (As we have [tex]10^2 = 8^2 + 6^2[/tex] )

That means the area of those triangles would be base times height times half, which comes as [tex]8 \times 6 \time 1/2 = 24[/tex] sq. units.

The three faces have area as= [tex]15 \times 10 + 15 \times 6 + 15 \times 8 = 15(24) = 360[/tex] sq. meters.

  • The two triangle faces have area = twice of 24 = 48.
  • surface area of triangular prism = 48 + 360 = 408

Sum of area of triangular prism and rectangular prism is 1550 + 408 = 1958 sq. meters

  • Common area is 10 times 15, its twice is 300,
  • so surface area of the composite figure is 1958 - 300 = 1658 sq. meters

Thus, the surface area of the considered composite solid is given by: Option B: 1658 sq. meters

Learn more about surface area here:

https://brainly.com/question/15096475

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