Class 8 Maths Mensuration Area of a General Quadrilateral

Area of a General Quadrilateral

To find the area of a quadrilateral, we can split it into two triangles by drawing one of its diagonals as shown in the given figure.                                                                           

 Class_8_Maths_Mensuartion_Quadrilateral

Now, area of quadrilateral ABCD = (area of Δ ABC) + (area of Δ ADC)

 

                                                      = (1/2) * AC * h1 + (1/2) * AC * h2

 

                                                      = (1/2) * AC * (h1 + h2)

 

                                                      = (1/2) * d * (h1 + h2)

 

where d denotes the length of diagonal AC.

 

Problem: 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.

Solution:

Here h1 = 13 m, h2 = 8 m and AC = 24 m

Area of quadrilateral ABCD = Area of Δ ABC + Area of Δ ADC

                                                 = 1/2 * b * h1 + 1/2 * b * h2

                                                 = 1/2 * b(h1 + h2)

                                                 = 1/2 * 24 * (13 + 8)

                                                 = 1/2 * 24 * 21

                                                 = 252 m2

Hence, required area of the field is 252 m2.

 Class_8_Maths_Mensuartion_Quadrilateral_1

Area of special quadrilaterals:

To find the area of rhombus, we can split it into two triangles by drawing one of its diagonals as shown in the given figure.

Area of rhombus ABCD = (area of ΔACD) + (area of ΔABC)

 

                                       = (1/2) * AC * OD + (1/2) * AC * OB

 

                                       = (1/2) * AC * (OD + OB)

                                     

                                       = (1/2) * AC * BD

 

                                      = 1/2 * d1 * d2

 

where AC = d1 and BD = d2

 Class_8_Maths_Mensuartion_Rhombus

Problem: The diagonals of a rhombus are 7.5 cm and 12 cm. Find its area.

Solution:

Given: d1 =7.5 cm and d2 = 12 cm

We know that,

Area of rhombus = 1/2 * d1 * d2

                               = 1/2 * 7.5 * 12

                               = 7.5 * 6

                               = 45 cm2

Hence, area of rhombus is 45 cm2.

 Class_8_Maths_Mensuartion_Rhombus_1

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