Geometry. (question from
apex)

D. A trapezoid and a semicircle.

Step-by-step explanation:

We have been given a composite figure. We are asked to find the best description of the shape of the figure.

A. A parallelogram and a circle.

Since opposite sides are not parallel, therefore, our given figure is not a parallelogram.

B. A rectangle and a semicircle.

We know that all angles of rectangle are right angles, but our figure has not any right angle, therefore, our given figure is not a rectangle.

C. A square and a circle.

We know that all angles of square are right angles and all sides are equal, but our figure has not any right angle, therefore, our given figure is not a square.

D. A trapezoid and a semicircle.

Upon looking at our given figure, we can see that it has a trapezoid on base and a semicircle on top, therefore, option D is the correct choice.

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!

i understand 100% 10/10 hit or miss?

step-by-step explanation: