Question

determine (a) the area and (b) the perimeter of the quadrilateral

7 yd
21 ft

a. the area of the quadrilateral is
(type a whole number.)
b. the perimeter of the quadrilateral is
(type a whole number.)

Explanation:

Step1: Convert units (optional, but check consistency)

Wait, the quadrilateral has length 21 ft and width 7 yd. First, convert yards to feet: 1 yd = 3 ft, so 7 yd = \(7\times3 = 21\) ft. Now it's a rectangle with length \(l = 21\) ft and width \(w = 21\) ft? Wait, no, maybe the original is a rectangle with length 21 ft and width 7 yd, but maybe it's a typo or same unit? Wait, no, let's check: the figure is a rectangle (four right angles), so area of rectangle is \(A = l\times w\). If length is 21 ft and width is 7 yd, we need to convert to same unit. 7 yd = 21 ft, so length and width are both 21 ft? Wait, no, maybe the width is 7 yd = 21 ft, so it's a square? Wait, no, 21 ft and 7 yd (21 ft) – so length 21 ft, width 21 ft? Wait, no, maybe the original is length 21 ft and width 7 yd, but let's assume we convert yd to ft: 7 yd = 21 ft. Then area is \(21\times21 = 441\) square feet? Wait, no, maybe the width is 7 yd, length 21 ft – no, that's inconsistent. Wait, maybe it's a rectangle with length 21 ft and width 7 yd, but we should convert to yards: 21 ft = 7 yd. So length 7 yd, width 7 yd? No, 21 ft is 7 yd (since 1 yd=3 ft, 21/3=7). So length 7 yd, width 7 yd? Wait, the figure has length 21 ft (7 yd) and width 7 yd. So it's a rectangle with length 7 yd and width 7 yd? No, 21 ft is 7 yd, so length 7 yd, width 7 yd? Wait, no, 21 ft is 7 yd, so length 7 yd, width 7 yd would be a square. Wait, the problem says quadrilateral, with right angles, so rectangle. So area is length × width. Let's take length as 21 ft and width as 7 yd. Convert 7 yd to ft: 7×3=21 ft. So length 21 ft, width 21 ft. So area is 21×21=441 square feet. Or if we take yards: length 7 yd, width 7 yd, area 49 square yards. But the answer is a whole number, so let's check the units. The problem has 21 ft and 7 yd – maybe it's a mistake, and both are in yards: 21 ft is 7 yd, so length 7 yd, width 7 yd? No, 21 ft is 7 yd, so length 7 yd, width 7 yd – area 49. Wait, no, 21 ft is 7 yd, so if length is 21 ft (7 yd) and width is 7 yd, then area is 7×7=49 square yards? Wait, no, 21 ft is 7 yd, so length 7 yd, width 7 yd – square. Then perimeter is 4×7=28 yards. But the problem says "21 ft" and "7 yd" – maybe it's a typo, and length is 21 ft (7 yd) and width 7 yd (21 ft). Wait, this is confusing. Wait, maybe the figure is a rectangle with length 21 ft and width 7 yd. Convert 7 yd to ft: 21 ft. So length 21 ft, width 21 ft. Area: 21×21=441 square feet. Perimeter: 2×(21+21)=84 feet. Or if in yards: length 7 yd, width 7 yd, area 49 sq yd, perimeter 28 yd. But the problem's answer is a whole number, so let's see: if length is 21 ft and width is 7 yd (21 ft), then area is 21×21=441, perimeter 2×(21+21)=84. Alternatively, maybe the width is 7 yd and length 21 ft, but 21 ft is 7 yd, so it's a square. Wait, the figure has length 21 ft and width 7 yd – maybe it's a rectangle with length 21 ft and width 7 yd, so convert 7 yd to 21 ft, so it's a square. So area is 21×21=441, perimeter 2×(21+21)=84.

Step1: Area of Rectangle

The quadrilateral is a rectangle (four right angles), so area \( A = \text{length} \times \text{width} \). Convert units to be consistent: 7 yd = \( 7 \times 3 = 21 \) ft (since 1 yd = 3 ft). Thus, length = 21 ft, width = 21 ft.
\( A = 21 \times 21 = 441 \) square feet.

Step2: Perimeter of Rectangle

Perimeter of a rectangle is \( P = 2 \times (\text{length} + \text{width}) \). Using length = 21 ft and width = 21 ft:
\( P = 2 \times (21 + 21) = 2 \times 42 = 84 \) feet.

Answer:

a. The area of the quadrilateral is \(\boxed{441}\) square feet (or if in yards, but based on conversion, 441 is correct).
b. The perimeter of the quadrilateral is \(\boxed{84}\) feet.

(Note: If units were intended to be yards, 7 yd and 7 yd (21 ft = 7 yd), area would be \(7 \times 7 = 49\) sq yd, perimeter \(2 \times (7 + 7) = 28\) yd. But the problem’s length is 21 ft, so converting width to ft gives 21 ft, leading to 441 and 84.)