Learners will use visualization, spatial reasoning, geometric modeling, and measurement to investigate the characteristics of figures, perform transformations, and construct logical arguments.

MAT-12.GM.04 Derive the formula A = ½ ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.

MAT-03.GM.M.07 Recognize area as an attribute of plane figures and understand concepts of area measurement.

MAT-03.GM.M.08 Find the area of a rectangle with whole-number side lengths by modeling with unit squares; show that area can be additive and is the same as found by multiplying the side lengths.

MAT-04.GM.M.05 Apply the area and perimeter formulas for rectangles, including connected rectangular figures, in problems.

MAT-05.GM.M.02 Find the area and perimeter of a rectangle, including connected rectangular figures, with fractional side lengths.

MAT-06.GM.AV.01 Derive the relationship of the areas of triangles using the area of rectangles. Calculate the areas of triangles and quadrilaterals in authentic and mathematical problems by composing and/or decomposing them into rectangles
and triangles.

MAT-06.GM.GF.03 Represent three-dimensional figures using nets made up of rectangles and triangles (right prisms and pyramids whose bases are triangles and rectangles). Calculate the surface area of prisms with rectangular and triangular
bases using nets. Apply these techniques in the context of solving authentic and mathematical problems.

MAT-07.GM.AV.02 Calculate areas of polygons by composing and/or decomposing them into rectangles and triangles, including in authentic problems. Solve problems involving the surface area of prisms and right pyramids using nets, including
authentic problems.

MAT-10.GM.30 Compute perimeters of polygons and areas of triangles, parallelograms, trapezoids, and kites using coordinates.

MAT-12.GM.04Derive the formula A=1 ab sin C for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.