A farmer has a square plot of land where he wants to grow five different crops at a time. In half of the area in the middle he wants to grow wheat but in rest four equal triangular parts he wants to grow different crops.
A) Explain by diagram how he can divide the area to fulfill his purpose.
B) For the same base and between the same parallels write the relation between area of triangle and parallelogram formed.

Question

A farmer has a square plot of land where he wants to grow five different crops at a time. In half of the area in the middle he wants to grow wheat but in rest four equal triangular parts he wants to grow different crops.
A) Explain by diagram how he can divide the area to fulfill his purpose.
B) For the same base and between the same parallels write the relation between area of triangle and parallelogram formed.

Vedantu Content Team · Accepted Answer

Hint: As the farmer needs to grow five different crops so he has to divide the square field into five parts by taking the midpoints of the sides of the square field and joining them.Area of triangle= $\dfrac{1}{2}$X area of parallelogramAs area of parallelogram=$base \times height$Therefore, Area of a triangle=$\dfrac{1}{2} \times base \times height$.Complete step-by-step answer:A) Let ABCD is a square field where the farmer wants to grow five different crops.As on half of the area in the middle of the square field ABCD, the farmer wants to grow wheat but in rest four equal triangular parts he wants to grow other four different crops.So we first mark the midpoints of the sides of square field ABCD i.e. P, Q, R and S of the respective sides AB, BC, CD and DA.Now join the points P, Q, R and S such that the square field is divided into five parts so that the farmer can grow the five different crops.So in the middle field PQRS the farmer will grow Wheat and in the rest of the triangular parts (I, II, III and IV) the farmer will grow the rest of the four different crops.

B) For the same base and between the same parallels write the relation between area of triangle and parallelogram formed.Area of triangle= $\dfrac{1}{2}$X area of parallelogram.As area of parallelogram=$base \times height$Therefore, Area of a triangle=$\dfrac{1}{2} \times base \times height$.So, Area of four triangle= $4 \times \dfrac{1}{2} \times base \times height = 2 \times base \times height.$Note: As the farmer wants to grow five different crops at a time and in half of the area in the middle he wants to grow wheat but in rest four equal triangular parts he wants to grow different crops.So, first find out the middle points of the square field formed and join them to get the field divided into five parts.