Answer:
the area of the giraffe exhibit is 5600 square feet, and the perimeter is approximately 322.462 feet.
Explanation:
To calculate the area of the giraffe exhibit, we can divide it into two triangles: EFG and EHG.
First, let's calculate the area of triangle EFG. We can use the formula for the area of a triangle given the coordinates of three vertices:
Area of triangle EFG = 1/2 * |(x1(y2-y3) + x2(y3-y1) + x3(y1-y2))|
Using the coordinates E(0,100), F(60, 100), and G(100,20), we can substitute the values into the formula:
Area of triangle EFG = 1/2 * |(0(100-20) + 60(20-100) + 100(100-20))|
= 1/2 * |(0 + 60(-80) + 100(80))|
= 1/2 * |(0 - 4800 + 8000)|
= 1/2 * |(3200)|
= 1600 square feet
Next, let's calculate the area of triangle EHG using the same formula. Using the coordinates E(0,100), H(0,20), and G(100,20):
Area of triangle EHG = 1/2 * |(0(20-20) + 0(100-20) + 100(20-100))|
= 1/2 * |(0 + 0 - 8000)|
= 1/2 * |(-8000)|
= 4000 square feet
To find the total area of the giraffe exhibit, we add the areas of the two triangles:
Total Area = Area of triangle EFG + Area of triangle EHG
= 1600 + 4000
= 5600 square feet
Now, let's calculate the perimeter of the giraffe exhibit by adding the lengths of all sides.
Length of side EF = distance between E(0,100) and F(60,100) = 60 feet
Length of side FG = distance between F(60,100) and G(100,20) = 82.462 feet (approximated)
Length of side GH = distance between G(100,20) and H(0,20) = 100 feet
Length of side HE = distance between H(0,20) and E(0,100) = 80 feet
Perimeter = Length of side EF + Length of side FG + Length of side GH + Length of side HE
= 60 + 82.462 + 100 + 80
= 322.462 feet (approximated)
Therefore, the area of the giraffe exhibit is 5600 square feet, and the perimeter is approximately 322.462 feet.