Question

finding the area of a triangle

estimate. circle all problems that will have areas greater than 15 square units. then find the exact areas of only the problems you circled.

1
2
3
4

Explanation:

Step1: Recall area formula

The area formula for a triangle is $A=\frac{1}{2}bh$, where $b$ is the base and $h$ is the height.

Step2: Analyze triangle 1

For triangle 1, assume each grid - square is 1 unit by 1 unit. By counting the grid - squares, the base $b = 10$ units and the height $h=6$ units. Then $A_1=\frac{1}{2}\times10\times6$.

Step3: Calculate area of triangle 1

$A_1=\frac{1}{2}\times10\times6 = 30$ square units. Since $30>15$, we circle this triangle.

Step4: Analyze triangle 2

Counting the grid - squares, assume the base $b = 6$ units and height $h = 4$ units. Then $A_2=\frac{1}{2}\times6\times4=12$ square units. Since $12<15$, we do not circle this triangle.

Step5: Analyze triangle 3

Counting the grid - squares, assume the base $b = 8$ units and height $h = 6$ units. Then $A_3=\frac{1}{2}\times8\times6 = 24$ square units. Since $24>15$, we circle this triangle.

Step6: Analyze triangle 4

Counting the grid - squares, assume the base $b = 4$ units and height $h = 3$ units. Then $A_4=\frac{1}{2}\times4\times3=6$ square units. Since $6<15$, we do not circle this triangle.

Step7: List circled triangles' areas

We circled triangle 1 with area $A_1 = 30$ square units and triangle 3 with area $A_3=24$ square units.

Answer:

The areas of the circled triangles are 30 square units and 24 square units.