Question

17 The area of the trapezoid below is 420 cm'. Find the height. Round to the nearest tenth if the answer is in decimal form. cm cm cm

Answer 1

We can draw the trapezoid as follows

Recall that the area of a trapezoid of the shape

Is given by the formula

`((B+b)\cdot h)/(2)`

In our case, we have b=1/5, B = 2/7 and the area is 17/420. So we have the following equation

`(17)/(420)=(((2)/(7)+(1)/(5))\cdot h)/(2)`

so we need to solve this equation for h.

We start by solving this operation

`(2)/(7)+(1)/(5)`

Recall that given two fractions a/b and c/d we have

`(a)/(b)+(c)/(d)=(a\cdot d+c\cdot b)/(b\cdot d)`

Taking a=2, b=7, c=1 and d=5, we get

`(2)/(7)+(1)/(5)=(2\cdot5+1\cdot7)/(7\cdot5)=(17)/(35)`

So we have the equation

`(17)/(420)=((17)/(35)\cdot h)/(2)`

Now, recall that givens numbers a,b,c where b and c are not zero, we have that

`((a)/(b))/(c)=(a)/(b\cdot c)`

In our case, lets take a=17, b=35 and c=2. So we have

`((17)/(35))/(2)=(17)/(35\cdot2)=(17)/(70)`

So we have the equation

`(17)/(420)=(17)/(70)\cdot h`

We can divide both sides by 17, so we get

`(1)/(420)=(h)/(70)`

So if we multiply both sides by 70, we get

`h=(70)/(420)=(7)/(42)=(1)/(6)`

So the height of the trapezoid is h=1/6 cm.