The area of a parallelogram is 342 square cm. The sum of its bases is 36 cm. Each slanted side measures 20 cm. What is the height?

Question

The area of a parallelogram is 342 square cm. The sum of its bases is 36 cm.  Each slanted side measures 20 cm.  What is the height?

Theodore Abad · Accepted Answer

<mathjax>#19#</mathjax> cm <img src="https://tutor.hix.ai 
<mathjax>#AB + CD = 36#</mathjax> 
<mathjax>#AD = BC = 20#</mathjax> 
<mathjax>#AB*h = 342#</mathjax> 
The area of a parallelogram is given by <mathjax>#base*height#</mathjax> 
Opposite sides of a parallelogram are equal, so therefore <mathjax>#AB = 36/2 = 18#</mathjax> 
<mathjax>#18*h = 342#</mathjax> 
<mathjax>#h = 342/18 = 19#

Maverick Smith · Answer

undefined To find the height of the parallelogram, we can use the formula for the area of a parallelogram, which is given by the product of the base and the height. Since the sum of the bases is 36 cm and the slanted sides measure 20 cm each, we can deduce that each base measures half of the sum of the bases, which is $ \frac{36}{2} = 18 $ cm.

Now, let's denote the height of the parallelogram as $ h $ cm. We have:

$$ \text{Area} = \text{Base} \times \text{Height} $$

Substituting the given values:

$$ 342 \, \text{cm}^2 = 18 \, \text{cm} \times h $$

To find the height $ h $, we can rearrange the equation and solve for $ h $:

$$ h = \frac{342 \, \text{cm}^2}{18 \, \text{cm}} $$

$$ h = 19 \, \text{cm} $$

So, the height of the parallelogram is 19 cm.