The length of the shorter base in an isosceles trapezoid is 4 in, its altitude is 5 in, and the measure of one of its obtuse angles is 135°. Find the area of the trapezoid.

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eudora eudora · Answer 1 · 2019-05-23T14:55:04+02:00

Answer:

Area of trapezoid = 45 in²

Step-by-step explanation:

In a isosceles trapezoid attached length of shorter base is 4 in., its altitude is 5 in. and the measure of its obtuse angle is 135°.

We have to find the area of the trapezoid.

Area of trapezoid = [tex]\frac{1}{2}(\text{shorter base + longer Base})\times height[/tex]

Area of trapezoid = [tex]\frac{1}{2}(BC+AD)(AE)[/tex]

Now AD = BC + 2x = (4 + 2x)

tan45 = [tex]\frac{h}{x}=\frac{5}{x}[/tex]

1 = [tex]\frac{5}{x}[/tex]

x = 5 in

Therefore, AD = 4+(5×2) = 4 + 10

AD = 14 in

Now area of trapezoid = [tex]\frac{1}{2}(4+14)(5)[/tex]

= 9×5 = 45 in²

onyebuchinnaji onyebuchinnaji · Answer 2 · 2022-04-25T17:45:34+02:00

The area of the isosceles trapezoid of the given base length is and angle is determined as 45 in².

The area of the isosceles trapezoid is calculated as follows;

A = ¹/₂(small base length + large base length) x height

small base length = 4 in

Large base length is calculated as follows;

Large base length = 2b + 4

where;

tan 45 = 5/b

b = 5/1

b = 5 in

Large base length = 2(5) + 4 = 14 in

A = ¹/₂(4 + 14) x 5

A = 45 in²

Thus, the area of the isosceles trapezoid of the given base length is and angle is determined as 45 in².

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