Question

1. geometry

a. find the perimeter of the rectangle.

12 in 2 in

b. find the area of these figures.

4 in 6 in; 18 in (diameter of circle); triangle with base 15 in and height 8 in

c. find the volume of the rectangular prism.

10 in, 7 in, 6 in (dimensions of rectangular prism)

d. find the value of the side marked c.

right triangle with legs 3 in and 4 in, hypotenuse c

Explanation:

Step1: Calculate rectangle perimeter

$P = 2(l+w) = 2(12+2) = 28$ in

Step2: Calculate rectangle area

$A_{rect} = l \times w = 6 \times 4 = 24$ in²

Step3: Calculate circle area

Radius $r = \frac{18}{2} = 9$ in
$A_{circle} = \pi r^2 = \pi \times 9^2 = 81\pi$ in²

Step4: Calculate triangle area

$A_{tri} = \frac{1}{2} \times b \times h = \frac{1}{2} \times 15 \times 8 = 60$ in²

Step5: Calculate prism volume

$V = l \times w \times h = 10 \times 7 \times 6 = 420$ in³

Step6: Find hypotenuse via Pythagoras

$c = \sqrt{3^2 + 4^2} = \sqrt{9+16} = \sqrt{25} = 5$ in

Answer:

A. 28 inches
B. Rectangle: 24 square inches; Circle: $81\pi$ square inches; Triangle: 60 square inches
C. 420 cubic inches
D. 5 inches