Metric properties

1103055801

Level:

The rectangular box

A B C D E F G H

has edges of lengths

| A B | = 6 cm

| B C | = 4 cm

and

| A E | = 8 cm

. The point

S

is the center of the base

A B C D

as seen in the picture. Find the distance between the point

E

and the point

S

\sqrt{77} cm

3 \sqrt{10} cm

2 \sqrt{26} cm

10 cm

1103055802

Level:

The rectangular box

A B C D E F G H

has edges of lengths

| A B | = 6 cm

| B C | = 4 cm

and

| A E | = 8 cm

. The point

S

is the center of the left side face

A D H E

as seen in the picture. Find the distance between the point

F

and the point

S

2 \sqrt{14} cm

2 \sqrt{29} cm

2 \sqrt{17} cm

4 \sqrt{2} cm

1103055803

Level:

The rectangular box

A B C D E F G H

has edges of lengths

| A B | = 6 cm

| B C | = 3 cm

and the face diagonal of the length

| B G | = 5 cm

. Find the distance between the center of the top face

E F G H

and the center of the bottom base

A B C D

4 cm

6 cm

7.5 cm

\sqrt{61} cm

1103055804

Level:

The rectangular box

A B C D E F G H

shown in the picture has edges of lengths

| A B | = 6 cm

| B C | = 4 cm

and

| A E | = 8 cm

. Find the distance between the lines

A H

and

F C

6 cm

2 \sqrt{13} cm

0 cm

4 cm

1103055805

Level:

The rectangular box

A B C D E F G H

shown in the picture has edges of lengths

| A B | = 6 cm

| B C | = 4 cm

and

| A E | = 8 cm

. Find the distance between the lines

A B

and

H G

4 \sqrt{5} cm

8 \sqrt{2} cm

10 cm

8 cm

1103055806

Level:

The rectangular box

A B C D E F G H

shown in the picture has edges of lengths

| A B | = 6 cm

| B C | = 4 cm

and

| A E | = 8 cm

. Find the distance between the lines

E S_{F G}

and

D S_{B C}

, where

S_{F G}

is the center of

F G

and

S_{B C}

is the center of

B C

8 cm

10 cm

4 \sqrt{5} cm

8 \sqrt{2} cm

1103056001

Level:

The cube

A B C D E F G H

shown in the picture has edges of length

a

. Find the distance between the points

E

and

C

. Choose the correct expression for this distance:

a \sqrt{3}

\sqrt[3]{3}

a \sqrt{2}

\sqrt{3}

1103056002

Level:

The cube

A B C D E F G H

shown in the picture has edges of length

a = 6 cm

. Let

S

be the midpoint of the base

A B C D

. Find the distance between the points

H

and

S

3 \sqrt{6} cm

6 \sqrt{5} cm

3 \sqrt{5} cm

6 \sqrt{3} cm

1103056003

Level:

The cube

A B C D E F G H

shown in the picture has edges of length

a = 6 cm

. Let

S

be the midpoint of the edge

F G

. Find the distance between the points

E

and

S

3 \sqrt{5} cm

6 \sqrt{5} cm

\sqrt{5} cm

6 \sqrt{3} cm

1103056004

Level:

The cube

A B C D E F G H

shown in the picture has edges of length

a = 6 cm

. Let

S_{1}

be the midpoint of the diagonal

E D

and let

S_{2}

be the midpoint of the diagonal

C H

. Find the distance between the points

S_{1}

and

S_{2}

3 \sqrt{2} cm

6 \sqrt{2} cm

\sqrt{2} cm

6 \sqrt{3} cm

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