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Thanks, Chris Betz
SqFt Measurements Calculations:
1. Floor Area:
The floor area remains unchanged:Floor Area=Length×Width=26′×29′=754 square feet\text{Floor Area} = \text{Length} \times \text{Width} = 26′ \times 29′ = 754 \text{ square feet}Floor Area=Length×Width=26′×29′=754 square feet
2. Wall Areas:
a. Short Walls (26′ wide, 8′ high):
Each short wall has an area of:Area of one short wall=Width×Height=26′×8′=208 square feet\text{Area of one short wall} = \text{Width} \times \text{Height} = 26′ \times 8′ = 208 \text{ square feet}Area of one short wall=Width×Height=26′×8′=208 square feet
Total for both short walls:Total area of short walls=208×2=416 square feet\text{Total area of short walls} = 208 \times 2 = 416 \text{ square feet}Total area of short walls=208×2=416 square feet
b. Long Walls (29′ wide with vaulted ceiling):
The long walls have a trapezoidal shape. The base heights are 8 feet and 11.5 feet.
Area of one trapezoid:Area of one trapezoid=12×(Base1+Base2)×Height\text{Area of one trapezoid} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}Area of one trapezoid=21×(Base1+Base2)×Height Area of one trapezoid=12×(8′+11.5′)×29′=12×19.5′×29′=282.75 square feet\text{Area of one trapezoid} = \frac{1}{2} \times (8′ + 11.5′) \times 29′ = \frac{1}{2} \times 19.5′ \times 29′ = 282.75 \text{ square feet}Area of one trapezoid=21×(8′+11.5′)×29′=21×19.5′×29′=282.75 square feet
Total for both long walls:Total area of long walls=282.75×2=565.5 square feet\text{Total area of long walls} = 282.75 \times 2 = 565.5 \text{ square feet}Total area of long walls=282.75×2=565.5 square feet
3. Ceiling Area:
Sloped Length of the Ceiling:
- Height difference between the wall height (8′) and the peak height (11.5′):
Height difference=11.5′−8′=3.5′\text{Height difference} = 11.5′ – 8′ = 3.5’Height difference=11.5′−8′=3.5′
- Half of the length of the room (half of 29′):
Half-length=14.5′\text{Half-length} = 14.5’Half-length=14.5′
- Calculate the sloped length using the Pythagorean theorem:
Sloped Length=(14.5′)2+(3.5′)2=210.25+12.25=222.5≈14.92′\text{Sloped Length} = \sqrt{(14.5′)^2 + (3.5′)^2} = \sqrt{210.25 + 12.25} = \sqrt{222.5} \approx 14.92’Sloped Length=(14.5′)2+(3.5′)2=210.25+12.25=222.5≈14.92′
Area of One Side of the Ceiling:
Area of one side=Sloped Length×Width of the Room=14.92′×26′=388.0 square feet\text{Area of one side} = \text{Sloped Length} \times \text{Width of the Room} = 14.92′ \times 26′ = 388.0 \text{ square feet}Area of one side=Sloped Length×Width of the Room=14.92′×26′=388.0 square feet
Total Ceiling Area (Both Sides):
Total Ceiling Area=388.0×2=776.0 square feet\text{Total Ceiling Area} = 388.0 \times 2 = 776.0 \text{ square feet}Total Ceiling Area=388.0×2=776.0 square feet