Question

100 POINTS EZ |

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.

Answer 1

Explanation:

Divide the quadrilateral field into two triangles by its diagonal.

Area of a triangle is given by the equation 1/2*base*height.

The top triangle's area = 1/2*24*13 = 156 m^2

The bottom triangle's area = 1/2*24*8 = 96 m^2

Combining, the area of the field = 156 + 96 = 252 m^2

Answer 2

• Area of the quadrilateral=1/2×diagonal×(sum of perpendiculars)

Put the values

Area:-

`\\ \rm\Rrightarrow (1)/(2)(24)(8+13)`

`\\ \rm\Rrightarrow 12(21)`

`\\ \rm\Rrightarrow 252m^2`