## OGQR 2020: Question No. 221

The figure above shows a piece of cheese with a corner cut off to expose plane surface ABC. What is the area of surface ABC?

- AD = 10 centimetres
- The shape of the cheese was a cube before the corner was cut off

Source | OGQR 2020 |

Type | Data Sufficiency |

Topic | Geometry |

Sub-Topic | Cubes (3D)/Triangles |

Difficulty | Medium – Hard |

### Solution

__Steps 1 & 2: Understand Question and Draw Inferences__

__Steps 1 & 2: Understand Question and Draw Inferences__

In this question, we are given:

- A figure having a piece of cheese from which a corner has been cut off.
- The removed corner exposes the plane surface ABC.

We need to determine:

- The area of the surface ABC.

The surface ABC is in the shape of a triangle.

- Therefore, to find the area of ABC, we either need the length of all the 3 sides or length of 2 sides and angle between them.

With this understanding, let us now analyse the individual statements.

__Step 3: Analyse Statement 1__

__Step 3: Analyse Statement 1__

*“AD = 10 centimetres”*

From this statement, we cannot determine any information about the length of sides of the triangle.

Hence, statement 1 is not sufficient to answer the question.

__Step 4: Analyse Statement 2__

__Step 4: Analyse Statement 2__

*“The shape of the cheese was a cube before the corner was cut off”*

- From this statement, we can say that length of sides of the triangle are the face diagonals of the cube.
- And, all the diagonals will be of the equal length
- Hence, ABC is an equilateral triangle.

However, we cannot determine any information about the length of sides of the triangle.

Hence, statement 2 is not sufficient to answer the question.

__Step 5: Combine Both Statements Together (If Needed)__

__Step 5: Combine Both Statements Together (If Needed)__

From Statement 1:

- AD = 10 cm

From Statement 2:

- The length of sides of the triangle are the face diagonals of the cube.
- ABC is an equilateral triangle.

Combining both the statements:

- Side of the cube= 10 cm
- Length of face diagonal of the cube = √(10
^{2}+ 10^{2}) = 10√2 cm.

- Length of face diagonal of the cube = √(10

Now, we know the length of the side of the equilateral triangle. We can easily find the area of the surface ABC.

Since we could find the answer by combining both the statements, option C is the correct answer.

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