The perimeter of the given shape is 63.50 units and its area is 170.625 square units.
Step-by-step explanation:
Step 1:
First, we need to determine the distance between each of the points in the shape ABCDEFGH.
There are vertical lines and horizontal lines. The distances between vertical lines are found by calculating the difference in y values while for horizontal lines, the distances are found by calculating the difference between the x values.
Step 2:
Distance of line AB, 15 - 4.5 = 10.5,
Distance of line BC, 14 - 8 = 6,
Distance of line CD, 15 - 10 = 5,
Distance of line DE, 8 - 3 = 5,
Distance of line EF, 15 - 10 = 5,
Distance of line FG, 3 - (-2.25) = 5.25,
Distance of line GH, 15 - 4.5 = 10.5 and
Distance of line AH, 14 - (-2.25) = 16.25.
Step 3;
The area of ABCDEFGH = The area of ABGH - the area of CDEF.
The area of ABGH = Length × Width = AH × AB = 16.25 × 10.5 = 170.625 square units.
The area of CDEF = Length × Width = CD × DE = 5 × 5 = 25 square units.
The area of ABCDEFGH = 170.625 - 25 = 145.625 square units.
Step 4:
The perimeter of shape ABCDEFGH is just the sum of all its lines.
Perimeter of ABCDEFGH = 10.5 + 6 + 5 + 5 + 5 + 5.25 + 10.5 + 16.25 = 63.50 units.
