Trapezoid - hard example

Bases of the trapezoid are: 24, 16 cm. Diagonal 22, 26 cm.
Calculate its area and perimeter.

Correct answer:

S =  264 cm2
o =  67.9663 cm

Step-by-step explanation:

a=24 cm c=16 cm  u=22 cm v=26 cm w=a+c=24+16=40 cm  s=2u+v+w​=222+26+40​=44 cm  S=s⋅ (s−w)⋅ (s−u)⋅ (s−v)​=44⋅ (44−40)⋅ (44−22)⋅ (44−26)​=264 cm2

Try calculation via our triangle calculator.

S = 2a+c​⋅ h = 2w​⋅ h  h=2⋅ S/w=2⋅ 264/40=566​=13.2 cm  u2 = h2 +a12​  a1​=u2−h2​=222−13.22​=588​=17.6 cm a2​=a−a1​=24−17.6=532​=6.4 cm  b2 = h2  + a22​  b=h2+a22​​=13.22+6.42​≐14.6697 cm  c1​=v2−h2​=262−13.22​=5112​=22.4 cm c2​=a−c1​=24−22.4=58​=1.6 cm  d2 = h2  + c22​  d=h2+c22​​=13.22+1.62​≐13.2966 cm  o=a+b+c+d=24+14.6697+16+13.2966=67.9663 cm

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You need to know the following knowledge to solve this word math problem:

arithmeticplanimetricsbasic operations and conceptsGrade of the word problem

 
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