A farmer’s field is in the shape of quadrilateral with side lengths

MATHEMATICS · Subjective · CBSE · Mathematics · Heron's Formula · Heron's Formula

Problem

A farmer’s field is in the shape of quadrilateral

PQRS

with side lengths

PQ = 120\,\text{m},\; QR = 150\,\text{m},\; RS = 130\,\text{m},\; SP = 110\,\text{m}

. The diagonal

PR

200\,\text{m}

. (i) Find the area of

\triangle PQR

. (ii) Find the area of

\triangle PRS

. (iii) Hence, calculate the total area of the field

PQRS

. (iv) Fertiliser is sold in

25\,\text{kg}

bags, each of which is sufficient for

200\,\text{m}^2

. How many whole bags must the farmer buy to cover the entire field once?