Question

1. find the area of the shape below. justify your answer.

Explanation:

Step1: Identify the shape and formula

The shape is a triangle. The formula for the area of a triangle is $A = \frac{1}{2} \times base \times height$.

Step2: Determine base and height

From the grid, count the number of units for the base and height. Let's assume each grid square is 1 unit. The base of the triangle spans 8 units (from one end to the other along the top), and the height (vertical distance from the base to the opposite vertex) is 3 units? Wait, no, looking at the formula written earlier $\frac{1}{2} \times 8 \times 3$? Wait, no, maybe the base is 8 and height is 3? Wait, no, the formula in the image is $\frac{1}{2} \times 8 \times 3$? Wait, no, the user's image has $\frac{1}{2} \times 8 \times 3$? Wait, no, the initial written formula is $\frac{1}{2} \times 8 \times 3$? Wait, no, let's re - examine. If we look at the triangle on the grid, let's count the base: from the left - most point to the right - most point of the triangle's base, it's 8 units (assuming each grid square is 1 unit). The height: the vertical distance from the base to the bottom vertex of the triangle. Let's say the height is 3 units. Then using the area formula for a triangle $A=\frac{1}{2}\times base\times height$.

Step3: Calculate the area

Substitute the base ($b = 8$) and height ($h = 3$) into the formula: $A=\frac{1}{2}\times8\times3$. First, calculate $8\times3 = 24$, then $\frac{1}{2}\times24=12$.

Answer:

12 (assuming each grid square has a side length of 1 unit)