Area of a trapezoid, "A" = (1/2) ( b₁ + b₂) h ; ______________________________________________ or, write as: A = ( b₁ + b₂) h / 2 ; ___________________________________ in which: A = area; b₁ = length of "base 1" (choose either one of the 2 (two bases); b₂ = length of "base 2" (use the base that is remaining); h = height of trapezoid; ____________________________________________ From the information given: ___________________________ A = 100 m² ; h = 5 m b₁ = 10 m b₂ = x ___________________________ Find "x", which is: "b₂" ; __________________________ A = ( b₁ + b₂) h / 2 ; _____________________________ Plug in our known values; and plug in "x" for "b₂" ; and solve for "x" ; _________________________________________________________ 100 m² = [(10m + x) (5m)] / 2 ; Solve for "x" ; _________________________________________________________ (10m + x) (5m) = (2)* (100m²) ; _________________________________________________________ (5m) (10m + x) = 200 m² ; ___________________________________________ Note: The distributive property of multiplication: ____________________________________________ a(b+c) = ab + ac ; a(b−c) = ab <span>− ac ; </span>____________________________________________
We have: (5m) (10m + x) = 200 m² ; ____________________________________________ So: (5m) (10m + x) = (5m*10m) + (5m * x) ;
= 50m² + (5m)x ; _______________________________________________ → 50m² + (5m)x = 200m² ; _______________________________________________ Divide the ENTIRE equation by "5m" ; _______________________________________________ → { 50m² + (5m)x } / 5m = (200m² / 5m) ; _______________________________________________ → 10m + x = 40m ; ________________________________________________ Now, subtract "10m" from EACH side of the equation; to isolate "x" on one side of the equation; and to solve for "x" ; _______________________________________ → 10m + x − 10m = 40m − 10m ;
to get:
→ x = 30 m ; which is our answer. ___________________________________________________ Answer: 30 m ; (or, write as: "30 meters") . _____________________________________________________
