Question

justin cut out rectangles and a triangle and put them together to form a letter j.
what is the area of the letter justin made?
a = □ in²

Explanation:

Step1: Calculate the area of the large rectangle

The formula for the area of a rectangle is \(A = l\times w\). For the large rectangle with length \(l = 12\) in and width \(w = 5\) in, \(A_1=12\times5 = 60\) in².

Step2: Calculate the area of the small rectangle

For the small rectangle with length \(l = 5\) in and width \(w = 4\) in, using the area formula \(A = l\times w\), \(A_2 = 5\times4=20\) in².

Step3: Calculate the area of the triangle

The base of the triangle is equal to the width of the small rectangle (\(b = 4\) in) and the height is equal to the width of the large rectangle (\(h = 5\) in). The formula for the area of a triangle is \(A=\frac{1}{2}bh\). So \(A_3=\frac{1}{2}\times4\times5=10\) in².

Step4: Calculate the total area

The total area \(A\) of the letter \(J\) is the sum of the areas of the two rectangles and the triangle. \(A=A_1 + A_2+A_3\). Substitute \(A_1 = 60\), \(A_2 = 20\), and \(A_3 = 10\) into the formula: \(A=60 + 20+10=90\) in².

Answer:

\(90\)