Question

The diagonal of a four sided field is 44m the perpendiculars from the opposite vertices on this diagonal are 20m and 15m find the area of the field

Answer 1

Answer: 770 m²

Step-by-step explanation:

Let us name the four-sided field as ABCD. (Refer to the diagram)

Diagonal = AC = 44 m

Perpendicular from one vertex to the diagonal = BE = 15 m

Perpendicular from opposite vertex to the diagonal = DF = 20 m

Break the quadrilateral into two triangles - ΔABC and ΔADC

Area of ABCD = Area of ΔABC + Area of ΔADC

Area of ABCD = (1/2 × b × h₁) + (1/2 × b × h₂)

Area of ABCD = (1/2 × AC × BE) + (1/2 × AC × DF)

Area of ABCD = (1/2 × 44 m × 15 m) + (1/2 × 44 m × 20 m)

Area of ABCD = 1/2 × 44m × (15 m + 20 m)

Area of ABCD = 22 m × 35 m

Area of ABCD = 770 m²

∴ Area of the four-sided field = 770 m²