Question

triangles and parallelograms
a project, carlos must provide one cut - out paper model of each type triangle: acute, right, and obtuse. he sketches each triangle on graph paper before making the models.
what is the total area of the three triangles?
14 square units
13.5 square units
13 square units
12.5 square units

Explanation:

Step1: Recall triangle - 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: Identify bases and heights for each triangle

For each of the three triangles on the graph, count the number of grid - squares for the base and height. Then calculate the area of each triangle using the formula $A = \frac{1}{2}bh$.

Step3: Sum up the areas

Add the areas of the three individual triangles together to get the total area.
Assume the side - length of each grid - square is 1 unit.
Let's say the first triangle has base $b_1 = 3$ and height $h_1= 3$, so $A_1=\frac{1}{2}\times3\times3 = 4.5$ square units.
The second triangle has base $b_2 = 4$ and height $h_2 = 2$, so $A_2=\frac{1}{2}\times4\times2=4$ square units.
The third triangle has base $b_3 = 3$ and height $h_3 = 3$, so $A_3=\frac{1}{2}\times3\times3 = 4.5$ square units.
The total area $A=A_1 + A_2+A_3=4.5 + 4+4.5=13$ square units.

Answer:

13 square units