# Area Questions

**FACTS AND FORMULAE FOR AREA QUESTIONS**

**FUNDAMENTAL CONCEPTS :**

**I. Results on Triangles:**

**1. **Sum of the angles of a triangle is

**2. **The sum of any two sides of a triangle is greater than the third side.

**3. **Pythagoras Theorem : In a right - angled triangle,

**4. **The line joining the mid-point of a side of a triangle to the opposite vertex is called the median.

**5. **The point where the three medians of a triangle meet, is called Centroid. The centroid divides each of the medians in the ratio 2 : 1.

**6. **In an Isosceles triangle, the altitude from the vertex bisects the base.

**7. **The median of a triangle divides it into two triangles of the same area.

**8. **The area of the triangle formed by joining the mid-points of the sides of a given triangle is one-fourth of the area of the given triangle.

**II.Results on Quadrilaterals :**

**1. **The diagonals of a parallelogram bisect each other

**2. **Each diagonal of a parallelogram divides it into two triangles of the same area.

**3. **The diagonals of a rectangle are equal and bisect each other.

**4. **The diagonals of a square are equal and bisect each other at right angles

**5. **The diagonals of a rhombus are unequal and bisect each other at right angles

**6. **A parallelogram and a rectangle on the same base and between the same parallels are equal in area.

**7. **Of all the parallelogram of given sides, the parallelogram which is a rectangle has the greatest area.

**IMPORTANT FORMULAE**

**I. **

**1. **Area of a rectangle = (length x Breadth)

**2. **Perimeter of a rectangle = 2( length + Breadth)

**II. **Area of square =

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

**IV. **

**1. **Area of a triangle =

**2. **Area of a triangle = , where a, b, c are the sides of the triangle and

**3. **Area of an equilateral triangle =

**4. **Radius of incircle of an equilateral triangle of side

**5.** Radius of circumcircle of an equilateral triangle of side

**6. **Radius of incircle of a triangle of area and semi-perimeter ** **

**V. **

**1.** Area of a parallelogram = (Base x Height)

**2. **Area of a rhombus =

**3. **Area of a trapezium =

**VI. **

**1. **Area of a cicle = , where R is the radius.

**2. **Circumference of a circle = .

**3. **Length of an arc = , where is the central angle.

**4. **Area of a sector = =

**VII. **

**1. **Area of a semi-circle =

**2. **Circumference of a semi - circle =

A) 65.25 | B) 56.25 |

C) 65 | D) 56 |

Explanation:

let each side of the square be a , then area = a x a

As given that The side is increased by 25%, then

New side = =

New area =

increased area=

Increase %= % = 56.25%

A) 55% | B) 65% |

C) 75% | D) 85% |

Explanation:

Let original radius = R.

New radius = =

Original area = and new area =

Decrease in area = = 75%

A) 30 | B) 40 |

C) 50 | D) 60 |

Explanation:

Let the side of the square(ABCD) be x meters.

Then, AB + BC = 2x metres.

AC = = (1.41x) m.

Saving on 2x metres = (0.59x) m.

Saving % = = 30% (approx)

A) 110 | B) 120 |

C) 130 | D) 140 |

Explanation:

let length = x and breadth = y then

2(x+y) = 46 x+y = 23

x²+y² = 17² = 289

now (x+y)² = 23²

x²+y²+2xy= 529

289+ 2xy = 529

xy = 120

area = xy = 120 sq.cm

A) 136 | B) 236 |

C) 336 | D) 436 |

Explanation:

let ABCD be the given parallelogram

area of parallelogram ABCD = 2 x (area of triangle ABC)

now a = 30m, b = 14m and c = 40m

Area of triangle ABC =

= = 168sq m

area of parallelogram ABCD = 2 x 168 = 336 sq m