Question

In the rectangular coordinate system above the area of pqr is what fraction of the area of lmn

Answer 1

In the rectangular coordinate system above the area of PQR is what fraction of the area of LMN

From the attached figure we find the area of PQR and area of LMN

WE know the formula for area of triangle = $\frac{1}{2}$ * base * height

In the triangle PQR,

Base PR= 4

Height = distance between x- axis and point Q = 4

Area of the triangle PQR = $\frac{1}{2}$ * 4 * 4 = 8

Similarly we find the area of LMN

In the triangle LMN,

Base LN= 12

Height = distance between x- axis and point M = 12

Area of the triangle LMN = $\frac{1}{2}$ * 12 * 12 = 72

Hence , $\frac{area PQR}{Area LMN}$ = $\frac{8}{72} = \frac{1}{9}$

Area of PQR = $\frac{1}{9}$ of the area of LMN