# What is the area of the region enclosed by the lines x = y, x = 8 and y = 4

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### 2 Answers

The area of the region enclosed by the lines x = y, x = 8 and y = 4 has to be determined.

It can be seen that x = 8 is a vertical line and y = 4 is a horizontal line. The line x = 8 is perpendicular to the line y = 4. The point at which they intersect is (8, 4).

The lines x = y and x = 8 intersect at (8, 8) and the lines x = y and y = 4 intersect at (4, 4).

There is a right triangle formed by the three lines. The length of the perpendicular sides is 4 and 4. The area of the enclosed region is therefore (1/2)*4*4 = 8.

**The area of the region enclosed by the lines x = y, x = 8 and y = 4 is 8.**

The area of rigion enclosed by three lines:

x = y, x = 8 and y = 4 is a right angled triange having coordinates of the corners as :

(4,4) the intersection point of x=y and y=4

(8,8) the intersection point of x=y and x=8 and

(8,4) the intersection point of x=8 and y=4

the base and height of this right-angled triangle is 4 and hence the area is equal to 4*4/2 = 8

**The area of the region enclosed by the line x=y, x=8 and y=4 is 8**