Question

Class 9th
Mathematics
Chapter 8 - Quadrilaterals
Formulas Needed . Give 1 example for each Formuals

Note : Don't copy, Don't spam .

Quality answer with good explanation will be Brainliest .​

Answer 1

Answer:

Area of a Parallelogram Base x Height

Area of a Rectangle Length x Width

Area of a Square Side x Side

Area of a Rhombus (1/2) x Diagonal 1 x Diagonal 2

Area of a Kite 1/2 x Diagonal 1 x Diagonal 2

Area of a general Quadrilateral =1/2×diagonal×(Sum of the height of two triangles)

If the bisectors of angles of a quadrilateral enclose a rectangle, then show that it is a parallelogram.

L, M, N, K are mid-points of sides BC, CD, DA and AB respectively of square ABCD, prove that DL, DK, BM and BN enclose a rhombus.

PQRS is a parallelogram. PS is produced to meet M so that SM = SR and MR is produced to meet PQ produced at N. Prove that QN= QR.

ABCD is a trapezium in which AB is parallel to CD. If ∟A = 36° and ∟B = 81°, then find ∟C and ∟D.

Answer 2

Quadrilaterals :-

A Quadrilateral is a 2d figure made of of line segments. A figure having 4 sides is said to be a Quadrilateral.

Properties of any quadrilateral :-

• The angles of the quadrilateral add up to 360°
• The sum of the exterior angles is 360°.
• In a regular Quadrilateral, the exterior angles are of measures 90° each.

Parallelogram :-

A parallelogram is a special type of Quadrilateral in which :-

• The opposite sides are equal and parallel.
• Opposite angles are equal.
• Adjacent angles are supplementary (add up to 180°).
• Diagonals bisect each other (divide the diagonal into 2 equal parts).

Area :-

• The area of the parallelogram = base × height

Perimeter :-

• The perimeter of a parallelogram = 2(base + height)

Rhombus :-

A rhombus is also a parallelogram, as it shows the same properties as that of a parallelogram.

• The opposite sides are equal and parallel (as all sides of the rhombus are equal).
• Opposite angles are equal.
• Adjacent angles are supplementary.
• Diagonals bisect each other at 90°.

Area :-

• The area of a rhombus = ½ × Diagonal 1 × Diagonal 2

Perimeter :-

• The perimeter of the parallelogram = 4 × side (side + side + side + side)

Rectangle :-

A rectangle also comes under the parallelogram category.

• Opposite sides are equal and parallel.
• Opposite angles are equal (all the angles of the rectangle are equal).
• Diagonals bisect each other at 90° and are equal.

Area :-

• The area of a rectangle = length × breadth

Perimeter :-

• The perimeter of the rectangle = 2(length + breadth)

Square :-

The square is too categorised under the parallelogram.

• All sides of a square are equal  and parallel (opposite sides are equal).
• All angles are equal.
• Diagonals bisect each other and are equal.

Area :-

• The area of a square = side × side => (side)²

If the diagonal of the square is given and the area is to be found :-

$\sf area = \dfrac{ ({diagonal)}^{2} }{2}$

Perimeter :-

• The perimeter of a square = 4 × side (side + side + side + side)

Kite :-

A kite under certain conditions can be a parallelogram

• Adjacent sides are equal..
• Diagonals intersect at 90°.
• One pair of opposite angles are equal. (the angles where the unequal sides meet).

A kite is said to be a parallelogram, when it is in the form of a rhombus or a square as these 2 shapes satisfy the properties of the kite as well as that of the parallelogram's.

Area :-

• The area of the kite = ½ × Diagonal 1 × Diagonal 2

Perimeter :-

• Perimeter of the kite = 2(side1 + side2)

Trapezium :-

A trapezium has the following properties :-

• Angles add up to 360°.
• It has one pair of parallel sides and one pair of non parallel sides.
• Hence, it is not a parallelogram.

Isosceles trapezium :-

• An isosceles trapezium is one In which the non parallel sides are equal

Area :-

• The area of trapezium = ½ × height × (sum of parallel sides)

Perimeter :-

• Perimeter of the trapezium = sum of it's sides

Important points to note :-

• A square can be a rectangle and a kite but a rectangle cannot be a square and a kite can't be square too.
• A rhombus is a parallelogram and a kite, but a kite is not a rhombus.
• A rhombus, square, rectangle are all parallelograms.
• All squares are rhombuses but not all rhombuses are squares.