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The base and height of a triangle are each extended 2 cm. What is the area of the shaded region?

The base and height of a triangle are each extended 2 cm What is the area of the shaded region class=

Respuesta :

serajom
using the relations of triangles
x/8 = (x+2)/10
10x = 8x + 16
10x - 8x = 16
2x = 16
x = 8

let's get the area of the rectangle in the shaded region first.

A = base x height

2cm x 8cm = 16cm²


...now the smaller triangle

A = ½(base)(height)
A = ½(2)(2)
A =4/2
A = 2cm²

adding the 2 Areas we get...

16cm² + 2cm² = 18cm²




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The Area of shaded region is 18 square centimeter.

By using property of similar triangles.

[tex]\frac{x}{8} = \frac{x+2}{10}\\\\ 10x = 8x + 16\\10x - 8x = 16\\2x = 16\\x = 8[/tex]

Area of large triangle is,

                           [tex]Area =\frac{1}{2}*base*height\\\\Area=\frac{1}{2}*10*10\\\\Area=100/2=50[/tex]

Area of small triangle is,

                          [tex]Area=\frac{1}{2}*8*8\\\\Area=\frac{64}{2}=32[/tex]

Area of shaded region is, subtract area of small triangle from area of large triangle.

 Area of shaded region [tex]=50-32=18[/tex]

Thus, Area of shaded region is 18 square centimeter.

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