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mars1129 [50]
2 years ago
13

An isosceles trapezoid has base angles of 45° and bases of lengths 8 and 14. The area of the trapezoid is

Mathematics
2 answers:
Yuri [45]2 years ago
4 0
Area = 0.5 ( sum of two bases ) * height


height = (14- 8)/2 = 3


Area = 0.5 x 3 x (14 + 8 ) = 33 sq units
Mice21 [21]2 years ago
3 0

Answer:

Option A is correct.      

Step-by-step explanation:

Given an isosceles trapezoid has base angles of 45° and bases of lengths 8 and 14. we have to find the area of isosceles trapezoid.

An isosceles trapezoid has base angles of 45° and bases of lengths 8 and 14.

From the figure attached , we can see an isosceles trapezoid ABCD,

AB = 8cm and CD=14cm

So we have to find the value of AE which is the height of Trapezoid in order to find area.

In ΔAED

tan\angle 45 =\frac{AE}{ED}

⇒ AE=1\times 3

∴ AE = DE =3cm

\text{The area of the trapezoid=}\frac{h}{2}\times (a+b)

h=3cm, a=14cm, b=8cm

Area=\frac{3}{2}\times(14+8)=\frac{3}{2}\times 22=33 units^2

hence, \text{The area of the trapezoid is }33 units^2

Option A is correct.

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