Question

find the area of the quadrilateral formed by the lines y = 2 x + 3 ,y =0, x =4 and x = 6

Answer 1

area of quadrilateral = y + y × x + x
2x + 3 + 0 × 4 +6 = 5x × 10
x = 10 / 5 = 2

Answer 2

Answer:

26 square units.

Step-by-step explanation:

Given lines are

y = 2 x + 3

y =0

x =4

x = 6

Plot these lines on a coordinate plane.

At x=4,

y = 2 (4) + 3 = 11

At x=6,

y = 2 (6) + 3 = 15

So, the vertices of quadrilateral are (4,0), (6,0), (6,15) and (4,11).

This figure contains 1 rectangle with dimensions 2×11 and a triangle with base 2 and height 4.

The area of rectangle is

$Area=length \times width=2\times 11=22$

The area of triangle is

$Area=\frac{1}{2}\times base \times height=\frac{1}{2}(2\times 4)=4$

The area of quadrilateral is

22 + 4 = 26

Therefore, the area of quadrilateral is 26 square units.