Question

The shape below has perimeter $66.$ lengths $bc$ and $cd$ are equal. angles $d$ and $b$ are right. what is the area of the shape below? [asy] pair c=(0,0); int a=24; pair a=c (0, a); pair b=a (10,0); pair e=c-(0,a); pair d = e -(18,0); draw(c--a--b--c--d--e--c); draw(rightanglemark(c, a, b, 60)); draw(rightanglemark(c,e,d, 60)); label("$c$", c, w); label("$d$", a, nw); label("$e$", b, ne); label("$b$", e, se); label("$a$", d, sw); int f=1; pair f=(a c)/2; pair g=f-(f,0); pair h=f (f,0); pair i=(c e)/2; pair j=i-(f,0); pair k=i (f,0); draw(g--h); draw(j--k); label("$9$", (d e)/2, s); label("$5$", (a b)/2, n); label("$13$", (b c)/2, sse); label("$15$", (d c)/2, nnw); [/asy]

Answer 1

The area of the shape is 70 square units.

Step-by-step explanation:

To find the area of the shape, we first need to find the lengths of the sides. Since angles D and B are right angles and lengths BC and CD are equal, we can conclude that the shape is a rectangle. The perimeter of a rectangle is equal to twice the sum of its length and width, so we can write the equation 2(AB+AD) = 66. Simplifying this equation gives us AB+AD = 33. Since AB = 5 and AD = 9 (given in the diagram), we can substitute these values into the equation to find the length of the other two sides. This gives us 5 + 9 = 14, so the width of the rectangle is 14. The area of a rectangle is equal to the product of its length and width, so the area of this shape is 5*14 = 70 square units.