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# Area Aptitude Question and Answer with Explanation

## Best explanation to understand and solve the area problems.

In this section, we will learn about the aptitude topic AREA. This topic is well known by everyone because we have learned a lot about this in our school days.

This has a various set of topics to cover. The most important point to remember in area is that you need to know all the formulas of the shapes. This is a challenging task.

We have given detailed explanations of different terms in area along with its formulas.

It will help you to learn the formulas easily and you can score good marks in your exams.

Also we have a set of aptitude questions based on AREA. you can take up the test and practice for your exams.

### What is area?

Area is nothing but the measurement of the surface of the given shape.

What are the topics under area aptitude?

There are three important topics in area aptitude. They are as follows.

2. Circles
3. Triangles

These are nothing but shapes with four sides. For eg: square, rectangle, parallelogram,etc.

Circles:

A circle is nothing but the locus of all points equidistant from a central point.

Triangles:

These are shapes with three angles.

### What are the formulas to calculate area of quadrilaterals?

i. Area of a rectangle = Length x Breadth

(Diagonal) 2 = (Length) 2 + (Breadth) 2

Perimeter of a rectangle = 2(Length + Breadth)

ii. Area of Parallelogram:

If a, b, c, and d are the lengths of a parallelogram,

S = 1/2 * (a + b + c + d)

Area = 2s(s - a)(s - b)(s - c)(s - d)

iii. Area of a square: (side)2 = 1/ 2 *(diagonal)2

Perimeter of a square = 4 x side

Area of Rhombus = 1/2 × (Product of diagonals)

When d1 and d2 are the two diagonals, then the side of rhombus = 1/2 * d12+d22

v. Area of 4 walls of a room = 2 x (Length + Breadth) x Height.

vi. Area of Parallelogram = (Base x Height).

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

= 1/2 * (a+b)h

Where a, and b are the parallel sides of the trapezium and h is the perpendicular distance between the sides 'a' and 'b'.

Where k = (a-b), i.e., the difference between the parallel sides and c and d are the two non-parallel sides of the trapezium. Also,

S = (k + c + d) / 2

Area = 1/2 * (a + b), h = (a + b) / k

s(s - k)(s - c)(s - d)

### How to calculate area of circles?

(i) Circumference of a circle = 2πr

(ii) Area of Circle = πr2

(iii) Arc AB = 2r / 3600 , where ∠AOB= θ and O is the center.

(iv) Area of sector AOB = r2 / 3600

(v) Area of Sector AOB = 1/2 × arc AB × r

### How to calculate area of triangle?

(i) Area of triangle = (1/2) × Base × height

(ii) If a, b, c are the lengths of the sides of a triangle and s = 1/2 * (a+b+c):

Area of a triangle = s(s - a)(s - b)(s -c)

(iii) Area of an isosceles triangle = b / A * 4a2-b2

(iv) Area of equilateral triangle= 3 /4 ×(side)2

Perimeter of an equilateral triangle = 3 × side

### What are the quick methods to solve area aptitude?

1. Carpeting a Floor:

(i) Length of the carpet required = (ii) Amount Required = Rate per meter × 2. Paving with tiles:

(i) Number of tiles required = (ii) The side of the largest possible square tile = HCF of length and breadth of the room.

3. Path around a garden, verandah around a room.

(i) When verandah is outside the room, surrounding it

Area of verandah = 2 (width of verandah) x [length + breadth of room + 2(width of verandah)].

(ii) When the path is within the garden, surrounded by it

Area of path = 2(width of path) x [length + breadth of garden - 2(width of path)].

(iii) When the area of the path is given, to find the area of the garden enclosed (the garden is square in shape).

Area of square garden = 4. Rhombus

(i) Area of a rhombus = 1/2 * (product of diagonals) 5. If the length and breadth of a rectangle is increased by x and y percent respectively, the area is increased by .

6. If all the measuring sides of any two-dimensional figure is changed by x%, its area changes by .

7. If all the measuring sides of any two-dimensional figure are changed (increased or decreased) by x%, its perimeter also changes by x%.

8. If all the sides of a quadrilateral are increased by x%, its corresponding diagonals also increased by x%.

9. If the area of a square is x cm2, the area of the circle formed by the same perimeter is given by .

10. Area of a square inscribed in a circle of radius r is 2r2.

11. The area of the largest triangle inscribed in a semicircle of radius r is r2.

These are the very important formulas that you need to know before attending area aptitude.

This will be an easy task since many of you would have learned most of these topics in your higher secondary school.

The only hard part is that you need to memorise all these formulas which will be a little confusing. But when you practice a lot, you will get used to the formulas and yes you can easily score marks in your tests.

Don't forget that we have a wonderful set of aptitude in our website. This will be very useful for you to practice for your exams.

1.

Find the area of rectangle whose length is 17 cm and breadth is 122 cm ?

2.

What is the area of rectangle with length 18.6cm and breadth 12.8cm?

3.

Find the area of triangle whose base is 44 cm and height is 99 cm ?

4.

A fence is constructed around a rectangular courtyard, due to some reason the linear measurement of a fence reduce by 7% and wideness expand by 10%. Calculate the % change in area.

5.

What would be the Area of a Rectangle if its Length is 26 cm and width is 20 cm ?

6.

What would be the Area of Square if its Side is 90 cm ?

7.

What would be the Area of the Rectangular Garden if its Length is 20 cm and Width is 30 cm ?

8.

Find the area of rectangle whose length is 43 cm and breadth is 68 cm ?

9.

Giving a thread a shape of ring whose radius is 42 cm. If the thread is given a shape whose four side is same then calculate the side.

10.

What will be the area of the square with sides 336cm?

11.

Find the area of triangle whose base is 22 cm and height is 69 cm ?

12.

What would be the Area of a Square field if its Side equals to 40 cm ?

13.

Area of triangle is 56 cm^2 and base is 7 cm . Calculate the height of a triangle ?

14.

side of a right angle triangle is 114m,115m,and 116m then find area of the triangle?

15.

A man dig a field whose every side is same, after that another man expand every side by 10% then calculate the percentage increase in the area.

16.

For cultivation of oranges a field was chosen which is rectangular in shape , a 2 meter broad track is made along the field in the inner side of the field. If the area of the track is 416 m². Then calculate the area of the field including the track.

17.

The base of a right triangle is 4.5 cm and height is 6 cm . Calculate the area of a right triangle ?

18.

Find the area of the trapezium whose two parallel sides are 172.5 meter and 91.5 meter and the perpendicular distance between them is 27 meter.

19.

Area of a parallelogram is 56 cm^2 and base is 8 cm . Calculate the height of a parallelogram ?

20.

Area of four walls of a room of length is 6.2 cm and width is 5 cm . Calculate the area of 4 walls of a room ?

21.

The 3 side of a tent which is in triangular shape are 15 cm , 20 cm and 25 cm . Calculate the area .

22.

What is the altitude if the base is 20 cm and area of the parallelogram is 300 cm2 ?

23.

The perimeter of a triangle is 17 cm , the base of a triangle is 4 cm and the hypotenuse is 8 cm . Calculate the height of a triangle ?

24.

What is the area of triangle whose base is 11 cm and height is 204 cm ?

25.

A brick measures 22 cm × 10 cm. How many such bricks will be needed in paving the floor of a rectangular room whose length and breadth are 11m and 8m respectively?

26.

Find the area of triangle whose base is 154 cm and height is 12 cm ?

27.

The length of a rectangle is 10 cm. and its width is 6 cm. If the length is increased by 5 cm what will be the width of rectangle so that its area remains the same?