Question

1. find the area and perimeter of the figures below. be sure to show all your work and label your answers.

a) area: formula: a = 1/2bh 4 1/2×12×4 a = 24mm² 12mm and h = 4mm perimeter: p = 6 + 8.5+12 p = 26.5mm
b) area: formula: a = 1/2(b₁ + b₂)h perimeter:

Explanation:

Step1: Calculate area of triangle

For the triangle in part a), the area formula is $A=\frac{1}{2}bh$. Here $b = 12$ mm and $h=4$ mm. So $A=\frac{1}{2}\times12\times4=24$ mm².

Step2: Calculate perimeter of triangle

The perimeter of the triangle in part a) is the sum of its side - lengths. $P = 6 + 8.5+12=26.5$ mm.

Step3: Calculate area of trapezoid

For the trapezoid in part b), the area formula is $A=\frac{1}{2}(b_1 + b_2)h$. Here $b_1 = 8$ in, $b_2=15.5$ in and $h = 4$ in. So $A=\frac{1}{2}(8 + 15.5)\times4=\frac{1}{2}\times23.5\times4=47$ in².

Step4: Calculate perimeter of trapezoid

The perimeter of the trapezoid in part b) is the sum of its side - lengths. $P=8 + 5+6 + 15.5=34.5$ in.

Answer:

a) Area: $24$ mm², Perimeter: $26.5$ mm
b) Area: $47$ in², Perimeter: $34.5$ in