Question

What polygon is obtained by graphing the given system of inequalities? What is the area of the polygon bounded by the inequalities?

y ≥ 1
x ≥ 1
y ≤ 4
x ≤ 6

The polygon obtained by graphing the system of inequalities is a
A) triangle
B) trapezoid
C) square
D) rectangle
The area of the polygon bounded by the inequalities is ___square units.
A) 15
B) 16
C) 24
D) 25

Answer 1

Hello,
Vertex are (1,1),(1,6),(1,4),(6,1)


1) a rectangle ANSWER D

2) 5*3=15 ANSWER A

Answer 2

The polygon obtained by graphing the system of inequalities is:

D) Rectangle.

The area of the polygon bounded by the inequalities is:

A) 15 square units.

Explanation:

We are given a system of inequalities as:

y ≥ 1

x ≥ 1

y ≤ 4

x ≤ 6

• Now when we graph these inequalities in a coordinate plane ; we will obtain a rectangle as a region bounded by these inequalities whose vertex are marked in the graph.

Also,

Length of one side of rectangle=5 units.

and length of the other side of the rectangle= 3 units.

• Hence, the Area of rectangle so obtained is:

5×3=15 square units.