Question

name: david date: score: show your work!!!!! 1. find the perimeter of a triangle with sides 8 cm, 5 cm, and 7 cm. a) 18 cm b) 19 cm c) 20 cm d) 21 cm 2. find the area of a triangle with base 12 m and height 8 m. a) 24 m² b) 48 m² c) 96 m² d) 32 m² 3. find the perimeter of a rectangle with length 14 m and width 9 m. a) 23 m b) 34 m c) 40 m d) 46 m 4. find the area of a rectangle with length 15 ft and width 8 ft. a) 120 ft² b) 100 ft² c) 130 ft² d) 110 ft 5. find the perimeter of a trapezoid with sides 10 m, 14 m, 9 m, and 11 m. a) 40 m b) 42 m c) 44 m d) 46 m

Explanation:

Step1: Recall perimeter formula for triangle

The perimeter \(P\) of a triangle with side - lengths \(a\), \(b\), and \(c\) is \(P=a + b + c\). Given \(a = 8\mathrm{cm}\), \(b = 5\mathrm{cm}\), \(c = 7\mathrm{cm}\), then \(P=8 + 5+7=20\mathrm{cm}\).

Step2: Recall area formula for triangle

The area \(A\) of a triangle with base \(b\) and height \(h\) is \(A=\frac{1}{2}bh\). Given \(b = 12\mathrm{m}\), \(h = 8\mathrm{m}\), then \(A=\frac{1}{2}\times12\times8 = 48\mathrm{m}^2\).

Step3: Recall perimeter formula for rectangle

The perimeter \(P\) of a rectangle with length \(l\) and width \(w\) is \(P = 2(l + w)\). Given \(l = 14\mathrm{m}\), \(w = 9\mathrm{m}\), then \(P=2(14 + 9)=2\times23 = 46\mathrm{m}\).

Step4: Recall area formula for rectangle

The area \(A\) of a rectangle with length \(l\) and width \(w\) is \(A=lw\). Given \(l = 15\mathrm{ft}\), \(w = 8\mathrm{ft}\), then \(A=15\times8 = 120\mathrm{ft}^2\).

Step5: Recall perimeter formula for trapezoid

The perimeter \(P\) of a trapezoid with side - lengths \(a\), \(b\), \(c\), and \(d\) is \(P=a + b + c + d\). Given \(a = 10\mathrm{m}\), \(b = 14\mathrm{m}\), \(c = 9\mathrm{m}\), \(d = 11\mathrm{m}\), then \(P=10 + 14+9 + 11=44\mathrm{m}\).

Answer:

1. C. 20 cm
2. B. 48 m²
3. D. 46 m
4. A. 120 ft²
5. C. 44 m