Question

Jamal drew a blueprint of a playscape that he wants to install in the backyard for his kids on a coordinate grid. The overall space of the playscape will be rectangular. Jamal will form a border around the space with pavers and he will cover the space with small pebbles before he installs the equipment.

The coordinates of the rectangle on the blueprint are
.

Each unit on the coordinate grid represents 2 feet.

PART A

What is the perimeter of the playscape space, in feet?

feet
Question 2
PART B

What is the area of the playscape space, in square feet?

square feet

Answer 1

I don't see the rectangle coordinates in your message. Could you either type the four vertex coordinates (in order) or upload the blueprint image?

While I wait, here are the steps I'll use once you provide them so you know what I'll calculate:

1. Identify two adjacent vertices to get the length and width in grid units.
- If the rectangle is axis-aligned, the side lengths in grid units are simply the absolute differences in x and y coordinates: length_units = |x2 − x1|, width_units = |y2 − y1|.
- If the rectangle is rotated, use the distance formula between adjacent vertices: side_units = sqrt[(x2 − x1)^2 + (y2 − y1)^2].

2. Convert units to feet: 1 grid unit = 2 feet, so
- length_ft = length_units × 2
- width_ft = width_units × 2

3. Compute perimeter and area:
- Perimeter = 2 × (length_ft + width_ft)
- Area = length_ft × width_ft

Example (if the rectangle had vertices (−3, −2), (5, −2), (5, 4), (−3, 4)):
- length_units = |5 − (−3)| = 8 units → length_ft = 16 ft
- width_units = |4 − (−2)| = 6 units → width_ft = 12 ft
- Perimeter = 2(16 + 12) = 56 ft
- Area = 16 × 12 = 192 sq ft

Send the actual coordinates and I’ll compute the exact perimeter and area for your playscape.