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Consider the following prism.

Suppose the bases are regular hexagons with 4cm edges.

a.Find the lateral area.

b.Find the base area.

c.Find the total area.

d.Find the volume.

Short Answer

Expert verified
  1. The lateral area is120鈥塩尘2.
  2. Th base area is 243鈥塩尘2.
  3. The total area is(120+483)cm2 .
  4. The volume is1203鈥塩尘3 .

Step by step solution

01

Step 1. Given Information.

The bases of the regular hexagon are 4cm.

02

Step 2. Write the concept.

A prism is a polyhedron that has two equal, parallel sides called 鈥渂ases鈥 and its lateral sides are 鈥減arallelograms鈥.

A rectangular prism is a polyhedron with two congruent and parallel bases. It has 6 faces and all the faces are in rectangle shape and have 12 edges.

A right rectangular prism is a prism that has 6 faces that are rectangles and all angles are right angles.

An oblique prism in which the bases are not perpendicular to each other.

03

Step 3. Find the area.

The lateral area of the prism is given by,

尝补迟别谤补濒鈥夆赌碱谤别补=Height笔补谤补尘别迟别谤鈥夆赌塷蹿鈥夆赌塀补蝉别

Then,

尝补迟别谤补濒鈥夆赌碱谤别补=(64)5=245=120鈥塩尘2

04

Step 1. Given Information.

The bases of the regular hexagon are 4cm.

05

Step 2. Write the concept.

A prism is a polyhedron that has two equal, parallel sides called 鈥渂ases鈥 and its lateral sides are 鈥減arallelograms鈥.

A rectangular prism is a polyhedron with two congruent and parallel bases. It has 6 faces and all the faces are in rectangle shape and have 12 edges.

A right rectangular prism is a prism that has 6 faces that are rectangles and all angles are right angles.

An oblique prism in which the bases are not perpendicular to each other.

06

Step 3. Find the area.

The base area is given by,

叠补蝉别鈥夆赌碱谤别补=33s22

Then,

叠补蝉别鈥夆赌碱谤别补=33(4)22=243鈥塩尘2

07

Step 1. Given Information.

The bases of the regular hexagon are 4cm.

08

Step 2. Write the concept.

A prism is a polyhedron that has two equal, parallel sides called 鈥渂ases鈥 and its lateral sides are 鈥減arallelograms鈥.

A rectangular prism is a polyhedron with two congruent and parallel bases. It has 6 faces and all the faces are in rectangle shape and have 12 edges.

A right rectangular prism is a prism that has 6 faces that are rectangles and all angles are right angles.

An oblique prism in which the bases are not perpendicular to each other.

09

Step 3. Find the total area.

To find the total area, add the lateral area and double of base area.

Since,

叠补蝉别鈥夆赌碱谤别补=243cm2

And

尝补迟别谤补濒鈥夆赌碱谤别补=120鈥塩尘2

Then, total area of the prism is given in below.

120+2(243)=(120+483)cm2

10

Step 1. Given Information.

The bases of the regular hexagon are 4cm.

11

Step 2. Write the concept.

A prism is a polyhedron that has two equal, parallel sides called 鈥渂ases鈥 and its lateral sides are 鈥減arallelograms鈥.

A rectangular prism is a polyhedron with two congruent and parallel bases. It has 6 faces and all the faces are in rectangle shape and have 12 edges.

A right rectangular prism is a prism that has 6 faces that are rectangles and all angles are right angles.

An oblique prism in which the bases are not perpendicular to each other.

12

Step 3. Find the volume.

To find the volume, multiply the height by the base area.

Volume=叠补蝉别鈥夆赌碱谤别补Height

Since,

叠补蝉别鈥夆赌碱谤别补=243cm2

Then,

Volume=243(5)=1203鈥塩尘3

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