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