Question

1. find the perimeter and area of this parallelogram. dimensions are in millimeters. (bonus) what is the name of this shape? 20. find the perimeter and area of this triangle. dimensions are in millimeters.

Explanation:

Problem 19 (Parallelogram)

Step 1: Perimeter of Parallelogram

The formula for the perimeter of a parallelogram is \( P = 2(a + b) \), where \( a \) and \( b \) are the lengths of adjacent sides. Here, \( a = 15 \) mm and \( b = 15 \) mm.
\( P = 2(15 + 15) = 2\times30 = 60 \) mm.

Step 2: Area of Parallelogram

The formula for the area of a parallelogram is \( A = base \times height \). The base is 15 mm and the height is 14 mm.
\( A = 15\times14 = 210 \) mm².

Step 3: Name of the Shape

Since all sides are equal (both adjacent sides are 15 mm) and it's a parallelogram, this shape is a rhombus (a special type of parallelogram with all sides equal).

Step 1: Perimeter of Triangle

The perimeter of a triangle is the sum of all its sides. The sides are 40 mm, 41 mm, and 9 mm.
\( P = 40 + 41 + 9 = 90 \) mm.

Step 2: Area of Triangle

First, check if it's a right triangle (using Pythagorean theorem: \( a^2 + b^2 = c^2 \)). Let \( a = 9 \), \( b = 40 \), \( c = 41 \).
\( 9^2 + 40^2 = 81 + 1600 = 1681 \), and \( 41^2 = 1681 \). So it is a right triangle.
The formula for the area of a right triangle is \( A = \frac{1}{2} \times base \times height \). Using \( base = 40 \) mm and \( height = 9 \) mm:
\( A = \frac{1}{2} \times 40 \times 9 = 20 \times 9 = 180 \) mm².

Answer:

• Perimeter: \( 60 \) millimeters
• Area: \( 210 \) square millimeters
• (Bonus) Name: Rhombus

Problem 20 (Triangle)