Question

A brick oven has an opening as shown. What is the area of the entire opening?

Answer 1

The correct answer should be 13.5

hope that helped(:

Answer 2

`13.93ft^(2)`

Explanation:

The area of the opening will be the sum of the area of the two shapes shown which are rectangle and half ellipse:

`Area =Area_(rectangle)+(1)/(2) Area_(Ellipse)`

The area of the rectangle is:

`Area_(Rectangle)=a*b`

where:

`a=4ft\\b=2(1)/(2)ft`

we replace values(we convert the mixed fraction to improper fraction by multiplying the whole number part by the fraction's denominator, then add that to the numerator then write the result on top of the denominator.):

`Area_(Rectangle)=4*2(1)/(2) =4*(5)/(2)=10`

The area of the ellipse is:

`Area_(Ellipse)=a*b*\pi`

where:

`a=Radius1=1(1)/(4)ft\\b=Radius2=2ft\\`

Radius2 will be half the side of the rectangle

`Radius2=(4)/(2)=2`

we replace the values:

`Area_(Ellipse)=1(1)/(4) *2*\pi=(5)/(4)*2*\pi=(5)/(2)\pi =7.85`

we calculate now the total area:

`Area =Area_(rectangle)+(1)/(2) Area_(Ellipse)\\Area=10+(1)/(2)(7.85)=10+3.93=13.93ft^(2)`