(05.02)A doghouse is to be built in the shape of a right trapezoid, as shown below. HELP What is the area of the doghouse?

32.5 square feet
40 square feet
187.5 square feet
375 square feet

96 square feet.

Step-by-step explanation:

The area of quadrilateral ABCD is given by:

Area=bh

Where b=8 units is the base of the quadrilateral and h=12 units is the height.

We substitute the values to obtain:

Area=8*12=96.

Or

The area of a trapezoid is

The area of the dog house is 96 square feet

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!