- Area of special quadrilaterals
A) Triangulation :
A general quadrilateral can be split into two triangles by drawing one of its diagonals. This “triangulation” helps us to find a formula for any general quadrilateral.
Area of quadrilateral ABCD
= ( area of Triangle ABC )+(area of Triangle ADC)
`= (1/2 xx AC xx h_1 )` + `(1/2 xx AC xx h_2 )`
`= 1/2 xx AC xx (h_1+h_2 )`
`=1/2 d ( h_1 + h_2 )` where d denotes the length of diagonal AC.
B) Area of Special quadrilaterals :
We can use the same method of splitting into triangles (which we called “triangulation”) to find a formula for the area of a rhombus.
ABCD is a rhombus.
Therefore, its diagonals are perpendicular bisectors of each other.
Area of rhombus ABCD
= (area of D ACD) + (area of D ABC)
`= (1/2 xx AC xx OD)` + `(1/2 xx AC xx OB)`
`=1/2 xx AC` × `(OD + OB)`
`=1/2 xx AC xx BD`
`=1/2 d_1 × d_2` where AC = `d_1` and BD = `d_2`
In other words, area of a rhombus is half the product of its diagonals.
Diagram of the adjacent picture frame has outer dimensions = 24 cm × 28 cm and inner dimensions 16 cm × 20 cm. Find the area of each section of the frame, if the width of each section is same.
The diagonal of a quadrilateral shaped field is 24 m and the perpendiculars dropped on it from the remaining opposite vertices are 8 m and 13 m. Find the area of the field.