Find the perimeter and area of the shape below.: *
A) P = 36 in; A = 34 in2
B) P = 32 in; A = 85 in2
C) P = 38 in; A = 56 in2
D) P = 36 in; A = 68 in2
To find the perimeter of the shape, you need to add the lengths of all four sides.
A) P = 36 in; A = 34 in2
Since the area is less than the perimeter, this option is incorrect.
B) P = 32 in; A = 85 in2
Since the area is greater than the perimeter, this option is incorrect.
C) P = 38 in; A = 56 in2
If we split the quadrilateral into two triangles, we can see that the base is 14 in and the height is 8 in. The area of a triangle is 0.5 * base * height, so the area of one triangle is 0.5 * 14 * 8 = 56 in2. Therefore, the total area is 56 in2 x 2 = 112 in2. Since the perimeter is 38 in, this option is incorrect.
D) P = 36 in; A = 68 in2
If we split the quadrilateral into two triangles, we can see that the base is 8 in and the height is 17 in. The area of one triangle is 0.5 * 8 * 17 = 68 in2. Therefore, the total area is 68 in2 x 2 = 136 in2. The perimeter is 36 in, which matches the given value. This is the correct option.
Therefore, the answer is:
D) P = 36 in; A = 68 in2