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  • 14-05-2019
  • Mathematics
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find the area of the figure

find the area of the figure class=

Respuesta :

gmany
gmany gmany
  • 16-05-2019

Answer:

A = 252

Step-by-step explanation:

It's a trapezoid.

The formula of an area of a trapezoid:

[tex]A=\dfrac{b_1+b_2}{2}\cdot h[/tex]

b₁, b₂ - bases

h - height

(look at the picture)

Use the Pythagorean theorem to calculate the length x:

[tex]x^2+12^2=15^2[/tex]

[tex]x^2+144=225[/tex]            subtract 144 from both sides

[tex]x^2=81\to x=\sqrt{81}\\\\x=9[/tex]

Substitute:

[tex]b_1=9+12+9=30\\b_2=12\\h=12[/tex]

[tex]A=\dfrac{30+12}{2}\cdot12=(42)(6)=252[/txt]

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