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Find the area of the trapezoid. TOP 11ft, RIGHT4√3ft , BOTTOM 15ft ,LEFT 8ft

Find The Area Of The Trapezoid TOP 11ft RIGHT43ft BOTTOM 15ft LEFT 8ft class=

Sagot :

tanweeleong195oxyqwp

Answer:

[tex]52\sqrt{3} ft^{2}[/tex]

Step-by-step explanation:

Please refer to the attached picture.

First we will find the area of rectangle BCDE.

Area of Rectangle = Length x Breadth = DE x CD

= 11 x [tex]4\sqrt{3}[/tex]

[tex]=44\sqrt{3} ft^{2}[/tex]

Next we will find Area of Triangle ABE.

Area of Triangle = 0.5 x Base x Height

[tex]0.5*4*4\sqrt{3} \\=8\sqrt{3} ft^{2}[/tex]

Area of Trapezoid = Area of Rectangle + Area of Triangle

[tex]=44\sqrt{3} +8\sqrt{3} \\=52\sqrt{3} ft^{2}[/tex]

View image tanweeleong195oxyqwp

Answer:

A = 52[tex]\sqrt{3}[/tex] ft² ≈ 90.1 ft²

Step-by-step explanation:

the area (A) of a trapezoid is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )

where h is the perpendicular height and b₁ , b₂ the parallel bases

here h = 4[tex]\sqrt{3}[/tex] , b₁ = 15 , b₂ = 11 , then

A = [tex]\frac{1}{2}[/tex] × 4[tex]\sqrt{3}[/tex] × (15 + 11)

   = 2[tex]\sqrt{3}[/tex] × 26

   = 52[tex]\sqrt{3}[/tex] ft²

   ≈ 90.1 ft² ( to the nearest tenth )

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