Question

find the area and perimeter of each of the following shapes. show all of your steps!!!

1. area: __ perimeter: __

(figure 1: a trapezoid with sides 4.3 ft, 2.4 ft, 5 ft, 7 ft, and height 4 ft)

1. area: __ perimeter: __

(figure 2: a parallelogram with sides 4 yd, 3 yd, 3 yd, 4 yd, and height 2 yd)

1. area: __ perimeter: __

(figure 3: a parallelogram with sides 9 ft, 6 ft, 9 ft, 6 ft, and height 3.2 ft)

1. area: __ perimeter: __

(figure 4: a triangle with sides 5 mi, 7 mi, 4 mi, and height 2.8 mi (relative to the 7 mi side))

Explanation:

Problem 1: Trapezoid (2.4 ft, 7 ft, height 4 ft, sides 4.3 ft, 5 ft)

Step 1: Area of Trapezoid

The formula for the area of a trapezoid is \( A = \frac{(a + b)}{2} \times h \), where \( a \) and \( b \) are the lengths of the two parallel sides, and \( h \) is the height.
Here, \( a = 2.4 \) ft, \( b = 7 \) ft, \( h = 4 \) ft.
\( A = \frac{(2.4 + 7)}{2} \times 4 \)
\( = \frac{9.4}{2} \times 4 \)
\( = 4.7 \times 4 \)
\( = 18.8 \) square feet.

Step 2: Perimeter of Trapezoid

Perimeter is the sum of all sides.
Sides: 2.4 ft, 7 ft, 4.3 ft, 5 ft.
Perimeter \( = 2.4 + 7 + 4.3 + 5 \)
\( = 18.7 \) feet.

Step 1: Area of Parallelogram

The formula for the area of a parallelogram is \( A = base \times height \).
Base \( = 3 \) yd, height \( = 2 \) yd.
\( A = 3 \times 2 = 6 \) square yards.

Step 2: Perimeter of Parallelogram

Perimeter is \( 2 \times (length + width) \).
Length \( = 4 \) yd, width \( = 3 \) yd.
Perimeter \( = 2 \times (4 + 3) = 2 \times 7 = 14 \) yards.

Step 1: Area of Parallelogram

\( A = base \times height \).
Base \( = 9 \) ft, height \( = 3.2 \) ft.
\( A = 9 \times 3.2 = 28.8 \) square feet.

Step 2: Perimeter of Parallelogram

Perimeter \( = 2 \times (9 + 6) \)
\( = 2 \times 15 = 30 \) feet.

Answer:

Area: \( 18.8 \) square feet, Perimeter: \( 18.7 \) feet

Problem 2: Parallelogram (base 3 yd, height 2 yd, sides 3 yd, 4 yd)