Class 8 Maths Mensuration 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.

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.

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.

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.

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