Answer:
a) The dimensions of the garden are: 4.5 ft and 5 ft
b) 22.5 ft² of fencing material
c) The most precise name for the shape of the garden is a Rectangle
Explanation:
a) Jenna has a garden with coordinate A(2,-1), B(4,3), C(9,3), D(7,-1) where each unit is 1 foot.
What are the dimensions of the garden rounded to the nearest 10th? (Looking for the lengths of the sides)
When we are given coordinates, we find the dimensions using the formula
= √(x2 - x1)² - (y2 - y1)²
(x1 , y1) and (x2 - y2)
For side AB
A(2,-1), B(4,3)
= √(4 - 2)² + (3 - (-1))²
= √2² + 4²
= √4 + 16
= √20 units = √20 feet
= 4.472135955 feet
Approximately = 4.5 feet
For side BC
B(4,3), C(9,3)
= √(9 - 4)² + (3 - 3)²
= √5² + 0²
= √25
= 5 units = 5 feet
For side CD
C(9,3), D(7,-1)
= √(7 - 9)² + (-1 - 3)²
= √(-2)² + -4²
= √4 + 16
= √20 units = √20 feet
= 4.472135955 feet
Approximately = 4.5 feet
For side AD
A(2,-1), D(7,-1)
= √(7 - 2)² + (-1 - (-1))²
= √5² + (-1 + 1)²
= √5² + 0²
= √25
= 5 units = 5 feet
Therefore, the dimensions of the garden are: 4.5ft and 5 ft
b) If Jenna decides to buy fencing for the garden, how much fence material does she need to buy? (Free response)
To buy fencing material for the garden, we have to find the area of the garden
Formula = Length × Width
= 4.5 ft × 5 ft
= 22.5 ft²
Therefore, Jenna needs to buy 22.5 square feet of fencing material.
c) What is the most precise name for the shape of the garden?
From the above calculation, we can see that
Side AB = Side CD = 4.5 ft
Side BC = Side AD = 5 ft
Therefore, the most precise name for the shape of the garden is a Rectangle