Use a ruler to make any measurements you need to find the area of each shape.
Refer to your formulas to find out which measurements you will need. Record your
measurements in a table.
Calculate the area of each shape you used. Find the area of at least one shape by
composing a rectangle. Find the area of at least one shape by decomposing it into
simpler shapes. Record your calculations in a table.
Shape Area Formula Measurements Area
Example:
Square
A = s2 s = 2 in. A = 4 sq. in.
Shape | Area Formula | Measurements | Area
Rectangle | A = l x w | l = 6 cm, w = 4 cm | A = 24 sq. cm
Triangle | A = 0.5 x b x h | b = 5 cm, h = 8 cm | A = 20 sq. cm
Circle | A = πr^2 | r = 3 cm | A ≈ 28.27 sq. cm
Trapezoid | A = 0.5 x h x (b1 + b2) | h = 7 cm, b1 = 6 cm, b2 = 10 cm | A = 56 sq. cm
USE TRIANGLE AND HEXOGON
Shape | Area Formula | Measurements | Area
Triangle | A = 0.5 x b x h | b = 4 cm, h = 6 cm | A = 12 sq. cm
Hexagon | A = 6 x (s x a)/2 | s = 4 cm, a ≈ 30.4 cm (apothem length) | A ≈ 72.96 sq. cm
FIX THE HEXAGON STUFF
Shape | Area Formula | Measurements | Area
Triangle | A = 0.5 x b x h | b = 4 cm, h = 6 cm | A = 12 sq. cm
Hexagon | A = 6 x ((s^2 x √3)/4) | s = 4 cm (side length) | A = 41.57 sq. cm
make hexagon whole number
Shape | Area Formula | Measurements | Area
Triangle | A = 0.5 x b x h | b = 4 cm, h = 6 cm | A = 12 sq. cm
Hexagon | A = 6 x ((s^2 x √3)/2)) | s = 5 cm (side length) | A = 64.95 sq. cm (approximated to whole number, the accurate value is around 65)
Calculate the total area of the figure you designed. Show your work. Include the
correct units for area in your answer.
Describe in words how you calculated the area of each shape. Be sure to include
which formulas you used. For which polygon(s) did you compose a rectangle to find
the area? Which polygon(s) did you decompose into simpler shapes? Which simple
shapes did you use?
To calculate the total area of the figure, we add the areas of the triangle and the hexagon.
1. Triangle:
Area = 0.5 x base x height
Area = 0.5 x 4 cm x 6 cm = 12 sq. cm
2. Hexagon:
Area = 6 x ((side^2 x √3)/2)
Area = 6 x ((5 cm)^2 x √3)/2) ≈ 64.95 sq. cm
Total Area = Area of Triangle + Area of Hexagon
Total Area = 12 sq. cm + 65 sq. cm ≈ 77 sq. cm
To calculate the area of the triangle, we used the formula for the area of a triangle, which is 0.5 x base x height. For the hexagon, we used the formula for the area of a regular hexagon, which is 6 times the area of one of its equilateral triangles, given by 6 x ((side^2 x √3)/2).
In this case, we composed a rectangle to find the area of the triangle (as it was given with base and height values) and decomposed the hexagon into six equilateral triangles where the area formula for a triangle was applied.
Overall, the total area of the figure was calculated by adding the areas of the triangle and the hexagon together.
Calculate the total area of the figure you designed. Show your work. Include the
correct units for area in your answer.
Describe in words how you calculated the area of each shape. Be sure to include
which formulas you used. For which polygon(s) did you compose a rectangle to find
the area? Which polygon(s) did you decompose into simpler shapes? Which simple
shapes did you use? theses are separate questions
To calculate the total area of the figure, we need to add the areas of the triangle and hexagon together.
1. Triangle:
- Area = 0.5 x base x height
- Area = 0.5 x 4 cm x 6 cm = 12 sq. cm
2. Hexagon:
- Area = 6 x ((side^2 x √3)/4) (For a regular hexagon)
- Area = 6 x ((5 cm)^2 x √3)/4
- Simplifying, Area = 6 x (25 x √3)/4 = 6 x (25 x 1.732)/4 = 6 x 43.3/4 = 64.95 sq. cm
Total Area = Area of Triangle + Area of Hexagon
Total Area = 12 sq. cm + 64.95 sq. cm = 76.95 sq. cm
For the triangle, we used the formula for the area of a triangle by multiplying the base by height and dividing by 2. For the hexagon, we utilized the formula for finding the area of a regular hexagon by multiplying the square of the side length by the square root of 3, and then taking 1/4 of that product since we are only dealing with one of the equilateral triangles that make up the hexagon.
In this case, we composed a rectangle to find the area of the triangle using the base and height values directly. We decomposed the hexagon into six equilateral triangles and calculated the area of one triangle to find the total area of the hexagon.