Question

1. The length of one of the diagonals of a field in the form of a
quadrilateral is 42 m. The perpendicular distances of the
other two vertices from this diagonal are 12 m and 9 m
(as shown in Figure 1). Find the area of the field.​

Answer 1

Answer:

area of quadrilateral ABCD = 441 sq m

Step-by-step explanation:

let the quadrilateral be ABCD

AC is diagonal of length 42 m

perpendicular distance of the vertices to the diagonal are 12 m and 9 m

the diagonal divide the quadrilateral into 2 triangles

area of quadrilateral ABCD = ar ∆ABC + ar ∆ADC

= 1/2 × AC × h1 + 1/2 × AC × h2

h1 and h2 are distance from vertices to the diagonal AC

= 1/2 × AC ( h1 + h2)

= 1/2 × 42 ( 12 + 9)

= 21 × 21

= 441 sq m

area of quadrilateral ABCD = 441 sq m

hope you get your answer