Question

Find the area and perimeter of the following trapezoid. round to the nearest whole number

Answer 1

First, I will re-sketch the image

First, we need to find x

Using the trig. ratio

`\tan \theta=(opposite)/(adjacent)`
`\tan 45=(6)/(x)`

cross-multiply

`x\tan 45=6`
`x*1=6`
`x=6`

Next, we need to find y

Using the trig. ratio

`\sin \theta=(opposite)/(hypotenuse)`
`\sin 45=(6)/(y)`

cross-multiply

`y\sin 45=6`

Divide both-side of the equation by sin45

`y=(6)/(\sin 45)`
`y=8.485`

Area of a trapezoid is given by the formula;

`A=(1)/(2)(a+b)h`

From the sketch above,

a=12

b=24

h=6

substitute the value and then evaluate

`A=(1)/(2)(12+24)6`
`=108\text{ square unit}`

Perimeter is the distance around the shape

`\text{Perimeter}=8.485+12+8.485+24`
`\text{perimeter }\approx\text{ 53}`