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what is the lateral surface area of the solid (options in picture) please help!

What Is The Lateral Surface Area Of The Solid Options In Picture Please Help class=

Sagot :

Answer:  B) 320 square centimeters

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Explanation:

The base faces are the two triangles that are parallel to one another. We'll be ignoring those faces when computing the lateral surface area.

Instead, we focus on the three rectangles that form the sides. We can think standing the prism on one of the triangular faces, so that one triangle is the floor and the other triangle is the ceiling. The rectangular pieces are the walls of this room.

  • The bottom rectangle is 8 cm by 16 cm, so it has area 8*16 = 128 sq cm.
  • The rectangle on the right is 6 cm by 16 cm, so it has area of 6*16 = 96 sq cm.
  • The rectangle on the left is 6 cm by 16 cm, so it has area 6*16 = 96 sq cm.

The three areas then combine to 128+96+96 = 320 square cm which is the lateral surface area.

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As a different approach, we can use this formula

LSA = p*h

where LSA is the lateral surface area, p is the perimeter of the base polygon, h is the height of the prism.

The base triangle has sides of 8, 6 and 6. So the perimeter is p = 8+6+6 = 20 cm. The height is h = 16 cm. The LSA is therefore,

LSA = p*h = 20*16 = 320 square cm.

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