Question

step 1: break the figure into rectangles and triangles.
step 2: find the area of the rectangle: 6·10 = 60.
step 3: find the area of the triangles: \\( \frac { 1 } { 2 } \cdot 2 \cdot 6 = 6 \\).
step 4: add the areas together: 60 + 6 = 66 square centimeters.
which best describes quinns error?
the base of the triangle in step 1 should be 4 cm.
the area of the triangles in step 3 should be \\( \frac { 1 } { 2 } \cdot 2 \cdot 10 = 10 \\).
the areas in step 4 should be multiplied together instead of added together.
the area of the triangle in step 3 should be doubled since there are 2 triangles.

Explanation:

Step1: Analyze the problem

We need to find the error in Quinn's calculation of the area of the composite figure. The figure has a rectangle and two triangles.

Step2: Recall the area formulas

The area of a rectangle is \(A = l\times w\) (where \(l\) is length and \(w\) is width), and the area of a triangle is \(A=\frac{1}{2}\times b\times h\) (where \(b\) is base and \(h\) is height).

Step3: Check Quinn's steps

• Step 2: Area of the rectangle: \(A_{rectangle}=10\times6 = 60\space cm^{2}\) (correct).
• Step 3: Quinn calculated the area of one triangle as \(\frac{1}{2}\times2\times6=6\space cm^{2}\). But there are two triangles.
• Correct calculation for triangles:

The area of one triangle is \(A_{triangle}=\frac{1}{2}\times2\times6\). Since there are two triangles, the total area of the triangles is \(2\times(\frac{1}{2}\times2\times6)\) (or simply \(\frac{1}{2}\times2\times6+\frac{1}{2}\times2\times6\)).

Answer:

The area of the triangle in Step 3 should be doubled since there are 2 triangles.