Answer:
a) The perimeter of the rectangle =
= 22 units
b) The area of the rectangle
= 30 square units
Explanation:
We solve the above question using the formula
= √(x2 - x1)² + (y2 - y1)²
When we are given vertices (x1, y1) and (x2, y2)
The vertices: (-1, -2), (-6, -2), (-6, -8), (-1, -8)
We have to find the length of the sides
Side A
(-1, -2), (-6, -2)
= √(-6 - (-1))² +( -2 -(-2))²
= √-5² + 0²
= √25
= 5 units
Side B
(-6, -2), (-6, -8)
= √(-6 - (-6))² + (-8 - (-2))²
= √(-6 +6)² + (-8 +2)²
= √0² + -6²
= √36
= 6 units
Side C
(-6, -8), (-1, -8)
= √(-1 - (-6))² +(-8 - (-8))²
= √(-1 + 6)² + (-8 + 8)²
=√ 5² + 0²
= √25
= 5 units
Side D
(-1, -2), (-1, -8)
= √(-1 -(-1))² + (-8 - (-2))²
= √(-1 + 1)² + ( -8 + 2)²
= √0 + -6²
= √0 + 36
= √36
= 6 units
From the above calculation,
Side A = Side C = 5 units
Side B = Side D = 6 units
Hence, this polygon is a quadrilateral called the RECTANGLE.
Therefore:
a) The perimeter of the rectangle =
2L + 2W
= 2(5) + 2(6)
= 10 units + 12 units
= 22 units
b) The area of the rectangle
= Length × Width
= 5 units × 6 units
= 30 square units