1. the edge lengths of a right rectangular prism are 1 2 meter, 1 2 meter, and 3 4 meter. how many unit cubes with edge lengths of 1 12 meter can fit inside? 2. the base of a rectangular prism has an area of 1 8 ft2, and the height of the prism is 2 3 ft. what is the volume of the prism? 3. the edge lengths of a right rectangular prism are 2 3 meter, 1 4 meter, and 3 4 meter. how many unit cubes with edge lengths of 1 10 meter can fit inside?

1) 324 cubes can be fitted into the rectangular prism.

2) 1/12 cubic ft.

3) 125 cubes can be fitted into the rectangular prism.

Step-by-step explanation:

1)

The edge lengths of the prism are given as:

1/2 meter, 1/2 meter and 3/4 meter.

The formula for finding the volume of a rectangular prism is the following: Volume = Length×Height×Width, or V = L×H×W.

so here let L=1/2 meter, B=1/2 meter and H=3/4 meter

Hence, V=(1/2)×(1/2)×(3/4)=3/16 cubic meters.

Now let 'n' cubes can be fitted inside this rectangular prism.

Let 'v' denotes the volume of 1 cube.

Volume of a cube with side length 's' units is given by:

Here s=1/12 meter

Hence, volume of cube (v)=(1/12)×(1/12)×(1/12)=1/1728 cubic meter

Now V=n×v

Hence, 324 cubes can be fitted into the given rectangular pyramid.

2)

The base of a rectangular prism has an area of  1/8 square feet.

This means let the rectangular base has length L and base B such that L×B=1/8 square feets.

also height (H) of the rectangular prism=2/3 ft.

Hence volume of rectangular prism= L×B×H=(1/8)×(2/3)=1/12 cubic ft.

3)

The edge lengths of the prism are given as:

2/3 meter, 1/4 meter and 3/4 meter.

The formula for finding the volume of a rectangular prism is the following: Volume = Length×Height×Width, or V = L×H×W.

so here let L=2/3 meter, B=1/4 meter and H=3/4 meter

Hence, V=(2/3)×(1/4)×(3/4)=1/8 cubic meters.

Now let 'n' cubes can be fitted inside this rectangular prism.

Let 'v' denotes the volume of 1 cube.

Volume of a cube with side length 's' units is given by:

Here s=1/10 meter

Hence, volume of cube (v)=(1/10)×(1/10)×(1/10)=1/1000 cubic meter

Now V=n×v

Hence, 125 cubes can be fitted into the given rectangular pyramid.

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step-by-step explanation:

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proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc