Find the larger base of a rectangular trapezoid whose area = 48, height = 6 and the large side

| September 17, 2021 | education

Find the larger base of a rectangular trapezoid whose area = 48, height = 6 and the large side makes an angle of 45 degrees with the base.

Let a trapezoid ABCD be given, it is rectangular, angles <D = <C = 90º, <A = 45º. Let’s draw the height of the trapezoid VK = 6 cm. The smaller side is equal to the height CD = VK = 6 cm. The smaller base CB, the larger base AD, with AD = DK + AK. DK = CB. The area of ​​the trapezoid is 48 cm².
Expression for determining the area of ​​a trapezoid:
S = (AD + CB) * BK / 2.
AD + CB = 2 * S / BK = 2 * 48/6 = 16 cm.
Consider a triangle ABK, it is rectangular <K = 90º, <A = 45º, define the angle <B:
<B = 180-90-45 = 45º.
<B = <A means an isosceles triangle with base AB and sides AK = BK = 6 cm.
Let’s go back to the trapezoid:
AD + CB = 16 cm.
DK + AK + CB = 16 (Taking into account that DK = CB):
2СВ = 16-AK = 16-6 = 10.
SV = 10/2 = 5 cm.
AD = DK + AK = 5 + 6 = 11 cm.
Answer: the larger base of the trapezoid is 11 cm.



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