Question

find the perimeter and area.
1
2
p =
a =
p =
a =

Explanation:

1. For the parallelogram:

Perimeter (\(P\)):

Step1: Recall the formula for the perimeter of a parallelogram

The perimeter of a parallelogram \(P = 2(a + b)\), where \(a\) and \(b\) are the side lengths. Here \(a = 4\space cm\) and \(b=5\space cm\)
\(P = 2(4 + 5)\)

Step2: Calculate the value

\(P=2\times9 = 18\space cm\)

Area (\(A\)):

Step1: Recall the formula for the area of a parallelogram

The area of a parallelogram \(A=base\times height\). Here base \(b = 4\space cm\) and height \(h = 3\space cm\)
\(A=4\times3\)

Step2: Calculate the value

\(A = 12\space cm^{2}\)

2. For the triangle:

Perimeter (\(P\)):

Step1: Recall the formula for the perimeter of a triangle

The perimeter of a triangle \(P=a + b + c\). Here \(a = 15\space cm\), \(b = 4\space cm\), and assume the third side \(c\) (we can check using the fact that for a non - right triangle with sides \(a,b,c\), perimeter is sum of all sides. But if we consider the given sides \(15\space cm\), \(4\space cm\) and assume the base - related side. Wait, no, perimeter is just sum of all sides. If we assume the sides of the triangle are \(15\space cm\), \(4\space cm\) and using the fact that in a triangle, perimeter \(P=15 + 4+13\) (assuming the three sides are \(15\), \(4\) and \(13\) (since the base - related segments \(4\) and \(13\) are adjacent to the height, but for perimeter we sum all outer sides).
\(P=15 + 4+13\)

Step2: Calculate the value

\(P=32\space cm\)

Area (\(A\)):

Step1: Recall the formula for the area of a triangle

The area of a triangle \(A=\frac{1}{2}\times base\times height\). Here base \(b=(4 + 13)=17\space cm\) and height \(h = 12\space cm\)
\(A=\frac{1}{2}\times17\times12\)

Step2: Calculate the value

\(A = 102\space cm^{2}\)

Answer:

1. \(P = 18\space cm\), \(A=12\space cm^{2}\)
2. \(P = 32\space cm\), \(A = 102\space cm^{2}\)