Question

1. here is a shape.

what is the area of this shape?
area: square units
show or explain your thinking.
show or explain a different way to determine the area of the same shape.

1. here is the expression sol wrote to calculate the surface area of this rectangular prism.

sol
lxwxh
4x2x3
24 square centimeters
describe the mistake that sol made.
what is the surface area of this prism?
show or explain your thinking.

Explanation:

4.

a)

Step1: Divide the shape

Divide the shape into a rectangle and a triangle.

Step2: Calculate the area of the rectangle

The rectangle has a length of \(6\) units and a width of \(4\) units. The area of a rectangle is \(A = l\times w\), so \(A_{rectangle}=6\times4 = 24\) square units.

Step3: Calculate the area of the triangle

The base of the triangle is \(6\) units and the height is \(3\) units. The area of a triangle is \(A=\frac{1}{2}\times b\times h\), so \(A_{triangle}=\frac{1}{2}\times6\times3=9\) square units.

Step4: Sum the areas

The total area of the shape is \(A = A_{rectangle}+A_{triangle}\), so \(A = 24 + 9=33\) square units.

Step1: Use the method of counting full - and half - squares

Count the full - squares. There are \(27\) full - squares.
Count the half - squares. There are \(12\) half - squares. Since \(12\) half - squares make \(6\) full - squares (\(12\times\frac{1}{2}=6\)).

Step2: Sum the equivalent full - squares

The total area is \(27 + 6=33\) square units.

Sol calculated the volume (\(V = l\times w\times h\)) instead of the surface area. The formula for the surface area of a rectangular prism is \(SA=2(lw + lh+wh)\).

Answer:

\(33\)

b)