MBCP – trapezoid with bases ВС and MP, ВН and SK – trapezoid heights. ВН = 4 cm, ВС = 5 cm, КР = 10 cm

univerkov | April 2, 2021 | education

MBCP – trapezoid with bases ВС and MP, ВН and SK – trapezoid heights. ВН = 4 cm, ВС = 5 cm, КР = 10 cm, angle М is equal to 45 degrees. Find the area of the trapezoid and the side of the CP.

1) The area of the trapezoid is calculated by the formula S = 0.5 (BC + MP) * BH.
Find MP: MP = MH + HK + KP.
The MHB triangle is isosceles (angle BMH = 45 => angle MBH = 45), therefore MH = BH = 4. HK = BC = 5. We have: MP = 4 + 5 + 10 = 19.
Now we can calculate the area: S = 0.5 (5 + 19) * 4 = 48.
2) In a right-angled triangle CKP CP is the hypotenuse, therefore CP² = KC² + KP² = 16 + 100 = 116.
CP = √116 = 2√29.

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