## OGQR 2020: Question No. 218

What is the area, in square meters, of the building plot shown in the figure above?

- KM = MP = 30 meters
- JK = KL = LM = MN = NP = 15 meters

Source | OGQR 2020 |

Type | Data Sufficiency |

Topic | Geometry |

Sub-Topic | Polygons |

Difficulty | Medium |

### Solution

__Steps 1 & 2: Understand Question and Draw Inferences__

__Steps 1 & 2: Understand Question and Draw Inferences__

In this question, we are given:

- A diagram of the building plot

We need to find the area of the building plot.

Let us mark all the points of the building plot as shown.

- Area of the plot = Area of JLRS + Area of LMNR + Area of QRNP

= JL * LR + LM * MN + NP * QP (JLRS, LMNR, and QRNP are rectangles)

= JL * MN + LM * MN + NP * LM (LR = MN and LM = QP)

Hence, we need to find the lengths of JL, LM, MN, and NP.

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

__Step 3: Analyse Statement 1__

__Step 3: Analyse Statement 1__

*“KM = MP = 30 meters”*

- Area of the plot = JL * MN + LM * MN + NP * LM
- = JL * MN + LM (MN + NP)
- = JL * MN + LM * MP
- = JL * MN + LM * 30

However, we do not know the value of JL, MN, and LM.

Hence, we cannot find the answer from statement 1 alone.

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

__Step 4: Analyse Statement 2__

__Step 4: Analyse Statement 2__

“*JK = KL = LM = MN = NP = 15 meters”*

- JL = JK +KL = 15 +15 = 30meters
- We are already given the value of LM, MN, and NP and we found the value of JL.

Hence, we can find the answer from this statement.

Thus, statement 2 is sufficient to answer the question.

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

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

Since we could determine the answer from statement 2 individually, this step is not required.

Hence, the correct answer is option B.

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