Question

the area of a quadrilateral shape field is 252 metre square. the perpendiculars dropped on the opposite corners on a diagonal are 8 metre and 13 metre .find the length of a diagonal.

Answer 1

area of any Quadrilateral = 1÷2×d(p1+p2)
252 metre square = 1÷2×d(8 m +13m)
252 metre square = 1÷2×d ×21m
d = 252 metre square ×2÷21m
d =24m

Answer 2

Length of the diagonal is 24 m.

• The area of the quadrilateral ABCD is 252 sq. m

• The diagonal is BD and perpendiculars are drawn from A and C on BD.

• The lengths of the perpendicular is 8 m and 13 m.

Let , AM = 8 m and CN = 13 m

• Now the area of the Quadrilateral ABCD is the sum of triangle ABD and triangle BCD.

Area of triangle ABD = 1/2×BD×AM

Area of triangle BCD = 1/2×BD×CN

• Area of quad ABCD = Area of triangle ABD + Area of triangle BCD

252 = 1/2×BD×AM + 1/2×BD×CN

252 = 1/2×BD×(AM + CN)

252 = 1/2×BD×(8 + 13)

252×2 / 21 = BD

Now, BD = 24 m

• Length of the diagonal is 24 m.