Area Aptitude Test Paper 6

Answer: A

Explanation:

Let original length = X

Original breadth = Y

So, original area = XY
So, decrease in area = X*Y -

Answer: B

Explanation:

The perimeter: 2 (L + B) = 210 or L+ B = 105 ...... (i)

As per the question: (L - B) = 25 ....... (ii)

Solving the above two equations:

L + B = 105

B = 105 - L

Put the value of B in (ii).

L - (105 - L) = 25

L - 105 + L = 25

2L = 25 + 105

2L = 130

L = 65

So, - B = 105 - 65 = 40

Now, area of a rectangle: L *B= 65 * 40 = 2600 m²

Answer: D

Explanation:

Diagonal of a rhombus bisect and divide each other equally.

So, half of the given diagonal = 15 m.

Let the half of the other diagonal = X

So, as per the Pythagoras theorem: 15² + X² = 25²

                                  225 + X² = 625

                                  X² = 625 - 225

                                  X² = 400

                                  X = 20

So, the length of the other diagonal is double of X: 20 + 20 = 40 m.

Now, Area of a rhombus = 1/2 * (product of diagonals)

                             = 1/2 * 30 * 40
                             = 600 sq. m.

Answer: C

Explanation:

Area of a parallelogram = (Base * Height)

Let the length of the base is = X

Then, the altitude or height is = 2X

So, Area: X * 2X = 162 sq. m.

2X² = 162

X² = 81

X = 9 meters (length of the base).

Answer: A

Explanation:

Trapezium is a quadrilateral with one pair of parallel sides.

Let the length of the smaller side = 12x

Length of the bigger parallel side = 18x

Distance between parallel sides = 32 meters

Area of a trapezium = 1/2 * (sum of parallel sides) * distance between them.

So, as per the question: 1500 = 1/2 (12x +18x) * 30

                                  1500 = 1/2 * 30x * 30

1500 = 30x * 15

30x = 1500 /15

30x = 100

x= 100 /30 = 3.3 meters