Question

for a project, carlos must provide one cut - out paper model of each type of 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? 13 square units 14 square units 13.5 square units 12.5 square units

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: Identify bases and heights of each triangle

For the first triangle (top - most): Assume we can find a base and height by counting grid - squares. Let's say base $b_1$ and height $h_1$. Counting the grid - squares, if $b_1 = 3$ and $h_1 = 2$, then $A_1=\frac{1}{2}\times3\times2 = 3$.

Step3: Calculate area of the second triangle

For the second triangle (left - most right - angled one), if base $b_2=3$ and height $h_2 = 2$, then $A_2=\frac{1}{2}\times3\times2=3$.

Step4: Calculate area of the third triangle

For the third triangle (right - most), if base $b_3 = 5$ and height $h_3=3$, then $A_3=\frac{1}{2}\times5\times3 = 7.5$.

Step5: Calculate total area

$A = A_1+A_2+A_3=3 + 3+7.5=13.5$ square units.

Answer:

13.5 square units