Question

what is the area of the arrow shown? diagram of arrow with dimensions: rectangle part 16 in. long, 2 in. wide; total length 20 in.; triangle part 6 in. wide options: 44 in.², 52 in.², 80 in.², 56 in.²

Explanation:

Step1: Area of the rectangle

The rectangle has length 16 in and width 2 in. Area of rectangle is $length \times width = 16 \times 2 = 32$ in².

Step2: Area of the triangle

The triangle has base 6 in and height $20 - 16 = 4$ in. Area of triangle is $\frac{1}{2} \times base \times height = \frac{1}{2} \times 6 \times 4 = 12$ in². Wait, no, wait. Wait, the total length is 20, the rectangle is 16, so the triangle's base is 6 in (the height of the triangle part) and the height of the triangle (the horizontal length) is $20 - 16 = 4$? Wait, no, maybe I messed up. Wait, the arrow is a rectangle plus a triangle. The rectangle is 16 in long and 2 in wide. The triangle: the base of the triangle is 6 in (the vertical side) and the height of the triangle (the horizontal side) is $20 - 16 = 4$ in? Wait, no, actually, the triangle's base is 6 in (the vertical dimension) and the height (horizontal) is 4 in? Wait, no, let's re-examine. The total length from left to right is 20 in. The rectangle is 16 in long (from left to the start of the triangle). So the triangle's horizontal length is $20 - 16 = 4$ in? Wait, no, the triangle is a triangle with base 6 in (the vertical side) and height (horizontal) 4 in? Wait, no, maybe the triangle has base 6 in and height (the horizontal length) is 4 in? Wait, no, that can't be. Wait, maybe I made a mistake. Let's try again. The arrow is composed of a rectangle and a triangle. The rectangle: length = 16 in, width = 2 in. Area of rectangle: 16 2 = 32 in². The triangle: the base of the triangle is 6 in (the vertical side) and the height of the triangle (the horizontal side) is $20 - 16 = 4$ in? Wait, no, that would make the area of the triangle $\frac{1}{2} \times 6 \times 4 = 12$ in². Then total area would be 32 + 12 = 44? But that's one of the options. Wait, but let's check again. Wait, maybe the triangle's base is 6 in and the height is 4 in? Wait, or maybe the triangle is with base 6 in and height (the horizontal length) is 4 in. Wait, but let's see the dimensions. The total length is 20, rectangle is 16, so the triangle extends 4 in to the right. The vertical dimension of the triangle is 6 in. So the triangle is a triangle with base 6 in and height 4 in. So area of triangle is 0.5 6 4 = 12. Area of rectangle is 16 2 = 32. Total area 32 + 12 = 44. So that's 44 in².
Wait, but let's check again. Wait, maybe I messed up the triangle's dimensions. Alternatively, maybe the triangle has base 6 in and height (the horizontal length) is 4 in. Yes, that makes sense. So rectangle area: 162=32. Triangle area: 0.56*4=12. Total 32+12=44. So the answer should be 44 in².

Answer:

44 in²