Students solve real-world area problems for rectangles, for example computing the area of a rectangular plot of land (80 ft × 55 ft = 4,400 sq ft) and finding the area of a painting (16.9 in × 9.3 in = 157.17 sq in). The lesson repeatedly models area as length × width in word-problem contexts and mentions using multiplication to calculate area in the Wrapping Up section.

Students set up area = length × width and multiply mixed numbers to find area in real-world contexts, for example computing Peter's bedroom area using 13 1/2 × 6 2/3 to get 90 square feet. Students compute areas of rectangles with fractional side lengths in problems such as the jewelry box (9/10 × 2/5) and a quiz item asking for the area of a rectangle with sides 7/8 m and 4/5 m. Students practice the fraction and mixed-number multiplication skills needed to carry out these area calculations and solve related word problems.

Students compute area for rectangular figures in real-world contexts: they find the area of Ian's rectangular stand (given fractional side lengths) and Kasey's rectangular canvas by multiplying fractional length and width. The practice and test items require students to compute area with fractional dimensions and to include correct units for area. Several problems explicitly ask for area or perimeter of rectangles using fraction operations.

Students are given the area formula A = s^2 and asked to evaluate it for different side lengths (e.g., Cassandra's square patio with s = 3 and s = 4). Activity and practice pages ask students to compute the area of a square (e.g., side 13 in. → 169 in^2) and to apply area calculations in a real-world challenge (two square posters totaling less than 250 in^2). The lesson includes multiple exponent practice problems and uses A = s^2 to connect exponents to area.

Students decompose a parallelogram by cutting and reassembling its pieces to make a rectangle and then measure base and height to compute area (Activity 1). Students fit two triangles together to form rectangles or parallelograms to derive and use A = 1/2 b h and practice finding areas of right and non-right triangles (Activity 2). Students decompose kites, trapezoids, and other irregular polygons into triangles, rectangles, and squares (Activity 3) and use those decompositions to compute area. Students apply these techniques to real-world and mathematical problems (pool, sails, pavers, picture frame, house, garden) where they sketch, compute, convert units, and sum or subtract component areas.

Students cut a circle into wedge-shaped sections, rearrange the wedges to form a rectangle, measure the rectangle's length and width, and compute its area (Activity 3). Students use the relationship half the circumference × radius to compute the circle's area and then use algebraic substitution to derive and apply A = πr^2, calculating areas and semicircle areas in practice problems (Activities 3–4).

Students compute areas directly for rectangles and triangles (e.g., Mrs. Yee's fenced area: original 8x6 => area 48 ft² and enlarged 16x12 => area 192 ft²) and use the area formula for a right triangle in the Basic Skills Review (1/2 × 6 × 8 = 24). Students complete activities comparing original and scale drawings' lengths, perimeters, and areas (tables that ask for area calculations for original and scaled shapes) and learn that area changes by the square of the scale factor.

Students solve multiple problems that require finding area by decomposing shapes: they decompose trapezoids into a rectangle and two right triangles to find area (answer keys show area = 18 cm^2 and 10 cm^2). Students compute parallelogram area using base × height (A = 12 × 4 = 48) and find triangle areas using 1/2 × base × height (triangle area = 12). Real-world application problems ask students to compute fabric for a parallelogram quilt, area of a kite by decomposing into two triangles, and patio and fountain area/perimeter calculations using area formulas.

The Parent Plan skills list explicitly states that students will "Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes." The "Decompose a Polygon" station instructs students to break polygons (including parallelograms and trapezoids) into simpler shapes using cutouts and partition lines. The "Real-Life Area Problem" activity asks students to create and solve contextual problems that require calculating the area of various shapes using models and drawings.

Students decompose a trapezoid into a rectangle and a triangle and compute each area (5 × 4 and 1/2 × 3 × 4) to find the trapezoid area. Students use the triangle area formula (A = 1/2 bh) and rectangle/square area formulas repeatedly when finding areas of faces on nets for triangular prisms, square pyramids, cubes, and rectangular prisms. Students are asked to take apart kit solids, lay out nets, measure polygonal faces (triangles, rectangles, squares), compute each face area, and sum them to find surface area. Real-world contexts (how much wrapping paper to buy, painting a pyramid-shaped roof) require students to apply these area techniques to solve problems.

Students calculate the area of a triangular base using A = 1/2 b h and then use that area as B in V = B h to find the volume of a triangular prism (Activity 3). Students compute triangular areas when finding surface area of a square pyramid by using 4 × (1/2 × 6 × 5) for the lateral faces. The unit also asks students to draw nets (e.g., net of a triangular prism) and to compute surface area and fabric needed for a tent, applying triangle and rectangle area calculations in real-world contexts.

Students compute the area of triangular cross sections using A = 1/2 × b × h (Activity 3 and the triangular-prism volume problems). Students use rectangle and square area calculations when finding surface area of rectangular prisms and bases of pyramids (e.g., SA = 2LW + 2LH + 2WH and base area calculations for the square pyramid). Students apply these area computations in real-world contexts (packing mugs, paint for a toy box, volumes of prisms) to solve problems.

Students compute areas of triangles using the triangle area formula (A = 1/2 × b × h) in problems such as the candy-bar triangular cross section and triangular-prism volume questions. Students find areas of quadrilaterals and polygons when calculating surface area and volume in contexts like the trapezoidal prism, rectangular prism paint problem, and cube decorative-paper problem. Students draw and match nets and use nets to find surface area, which requires decomposing 3D solids into 2D faces made of rectangles and triangles.

Students select three preprinted nets and measure their faces on graph paper, then use provided area formulas (A = l × w, A = 1/2 × b × h, s^2, etc.) to compute surface area and volume. The Surface Area and Volume pages and the answer key show students calculating the surface area of a triangular prism by summing areas of its rectangular faces and triangular bases and the square pyramid by adding the base area plus four triangular face areas (4 × 1/2 × b × h). Students apply these calculations to shapes they assemble and report these areas/volumes as part of building a real-world model (robot/house/castle).

Students compute the area of a rectangular rug with mixed-number side lengths (6 2/3 feet by 3 1/2 feet) and the answer key shows the multiplication of converted improper fractions to get 23 1/3 square feet. The activity requires students to multiply fractional dimensions to produce an area measurement, demonstrating use of area = length × width with mixed numbers. Several word problems require multiplying mixed numbers, reinforcing the arithmetic used in area calculations.

Students solve explicit area problems for a right triangle (Problem 5: 16 mm base, 12 mm height), a parallelogram (Problem 4), a trapezoid that they are instructed to decompose into two triangles and a rectangle (Problem 6), and a square blanket word problem (Problem 7). The Parent Plan explicitly lists the skill: "Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes" and also lists applying area formulas in real-world and mathematical problems.

Students compute the area of a fuel cell (a square) from a given side length (4 ft) and use that area (16 ft²) to determine total floor area needed for multiple fuel cells (e.g., 119 cells → 1,904 ft²). Students also work with area in the supply-drop task by using the formula A = πr² to calculate the drop zone radius and the cost to build the drop zone from its area. The activity requires students to multiply areas by counts/costs to determine room size and construction cost.

Students calculate areas and use area measurements in real contexts: Activity 4 includes examples comparing tile packs by cost per square inch and rug/sod problems asking for dollars per square foot. The bonus task directs students to cut a piece of paper into a rectangle and a triangle, measure dimensions, and use the formulas Area = Length × Width and Area = 1/2 × Base × Height to compute areas and then compute area per inch of length. Several student pages and answer keys require computing area and using those areas to compare value (e.g., tile pack, rugs, sod).