# Find the area of right triangles, other triangles, special quadrilaterals, and polygons by

### Cluster

Solve real-world and mathematical problems involving area, surface area, and volume.

Evidence of Learning Statements

 Students with a level 1 understanding of this standard will most likely be able to: Students with a level 2 understanding of this standard will most likely be able to: Students with a level 3 understanding of this standard will most likely be able to: Students with a level 4 understanding of this standard will most likely be able to: Find the area of right triangles and rectangles. Find the area of right triangles and rectangles in contextual and mathematical problems. Find the area of a quadrilateral given its decomposition into rectangles and/or right triangles. Find the area of a non-right triangle. Find the area of triangles, quadrilaterals, and polygons that can be decomposed into parts utilizing common area formulas. Find the area of polygons embedded in real-world and mathematical problems. Find the area of complex polygons utilizing common area formulas by decomposing them into common shapes. Find the area of polygons embedded in complex real-world and mathematical problems.

Instructional Focus Statements

Level 3:

Students should work with drawings and models/manipulatives to gain an understanding that familiar shapes can be put together to create composite shapes, and unfamiliar shapes can be decomposed into non-overlapping, adjacent familiar shapes. In previous grades, students developed an understanding of how to find the area of a rectangle using an area model and generalize this concept to discover the area formula for a rectangle. Students should employ their understanding of finding the area of a rectangle to then decompose a rectangle into two right triangles to discover that the area of a right triangle is half the area of a rectangle. Therefore, discovering that the area of a right triangle is A= ½ bh. Students should use this knowledge, coupled with the understanding of composing and decomposing shapes, to build an understanding that the area of composite shapes is equal to the sum of the areas of the non-overlapping, adjacent shapes.

Level 4:

Students should interchangeably compose and decompose shapes to form familiar shapes. They use these to find the area of familiar shapes and the total area of the original composite shape. It is important that the student is able to verbalize that these are equivalent and explain why. In solidifying this concept, students should generalize that the area of a right triangle is half the area of a rectangle resulting in the formula A = ½ bh and explain this connection using precise mathematical vocabulary. Additionally, as students work with the same shape, they should be able to compare different decompositions to see that a shape can be decomposed in multiple ways and have the same area. This understanding should be transferred into solving mathematical and real-world problems by using precise mathematical vocabulary to explain their reasoning.