Question

problem 2 select all the triangles that have an area of 30 square units. grade 6 unit 1 mid - unit assessment - version a tennessee standards edit cc by - nc - sa download for free at openup.org

Explanation:

Step1: Recall triangle - area formula

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

Step2: Analyze option A

For option A, if $b = 6$ and $h = 10$, then $A=\frac{1}{2}\times6\times10=30$ square units.

Step3: Analyze option B

For an equilateral triangle with side - length $s = 10$, the height $h=\frac{\sqrt{3}}{2}s=\frac{\sqrt{3}}{2}\times10 = 5\sqrt{3}\approx8.66$. Then $A=\frac{1}{2}\times10\times8.66 = 43.3$ square units.

Step4: Analyze option C

If $b = 6$ and $h = 10$, then $A=\frac{1}{2}\times6\times10 = 30$ square units.

Step5: Analyze option D

It seems there is an error in the values provided. Assuming the base $b = 6$ and the height value is mis - written. If we use the correct height corresponding to the base, if $b = 6$ and $h = 10$, $A=\frac{1}{2}\times6\times10=30$ square units. But from the picture, the height value seems incorrect as marked.

Step6: Analyze option E

If $b = 3$ and $h = 10$, then $A=\frac{1}{2}\times3\times10 = 15$ square units.

Answer:

A. The triangle with base 6 and height 10 has an area of 30 square units.
C. The triangle with base 6 and height 10 has an area of 30 square units.