Warm-UpWhat are the 8 Standards of Mathematical Practices?

Make sense of problems and persevere in solving themReason abstractly and quantitativelyConstruct viable arguments and critique the reasoning of othersModel with mathematics

Use appropriate tools strategically

Attend to precision

Look for and make use of structure

Look for and express regularity in repeated reasoning

Today’s Objective:G.GPE.B.7 Use coordinates to

compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

Rectangle Area Conjecture:

The area of a rectangle is given by the formula ____________, where A is the area, b is the length of the base, and h is the height of the rectangle.

A = bh

Find the area of this shape

€

12(10) =5

€

12(6) =3

€

12(6) =3

€

12(18) =9

32

The area of the figure is 52 square units

Investigation: Area Formula for Parallelogram

A parallelogram

A straight edge

A compass

Scissors

• From the vertex of the obtuse angle adjacent to the base, draw an altitude to the side opposite the base. Label the parallelogram as shown.

Investigation: Area Formula for Parallelogram

• Cut along the altitude. You will have two pieces – a triangle and a trapezoid. Try arranging the two pieces into other shapes without overlapping them. Is the area of each of these new shapes the same as the area of the original parallelogram? Why?

• Is one of your new shapes a rectangle? Calculate the area of this rectangle. What is the area of the original parallelogram? State the conjecture.

Parallelogram Area Conjecture

The area of a parallelogram is given by the formula ____________________, where A is the area, b is the length of the base, and h is the height of the parallelogram.

A = bh

Let’s practice!!!A represents area and P represents perimeter.

A = 2508 cm2

P = ?

210 cm

Let’s practice!!!Find the area of the shaded region.

A = 42 ft2