Calculate the area of the figure below using the following information: area of triangle abc = 31.8 square units area of triangle acd = 39.2 square units area of triangle aed = 35.5 square units image of irregular pentagon with vertices points a, b, c, d, and e starting at upper left moving clockwise. two dotted diagonal lines, one connecting vertices a and c, and the second connecting vertices a and d. the area of the figure abcde is square units. answer for blank 1:

Area of irregular pentagon=106.5 square units.

Step-by-step explanation:

It is given that Area of triangle ABC = 31.8 square units,

Area of triangle ACD = 39.2 square units and

Area of triangle AED = 35.5 square units.

Thus, ABCDE makes an irregular pentagon, therefore

Area of irregular pentagon= Area of triangle ABC +Area of triangle ACD+Area of triangle AED

⇒Area of irregular pentagon=31.8+39.2+35.5

⇒Area of irregular pentagon=106.5 square units.

Thus, area of an irregular pentagon is 106.5 square units.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4