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? 12.5 square units 13 square units 13.5 square units 14 square units

Answer 1

The answer is B) 13

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Answer 2

Answer: 13.5 square units

Explanation: since we know that the area of a triangle =   $\frac{1}{2} (x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2))$

let us give the name to the triangles ABC having vertices (4,10), (5,7), and (7,8),  triangle DEF having vertices (3,6), (3,3) and (6,3) and triangle PQR having vertices (7,6), (7,1) and (9,4).

Thus,  Area of $\bigtriangleup$ ABC= $\frac{1}{2}$×(4(7-8)+5(8-10)+7(10-7))= $\frac{1}{2}$(-4-10+21)=8/2=4 unit.

Area of $\bigtriangleup$ DEF= $\frac{1}{2}$×(3(3-3)+3(3-6)+6(6-3))=$\frac{1}{2}$×(0-9+18)=9/2=4.5 unit.

Area of $\bigtriangleup$ PQR= $\frac{1}{2}$×(7(1-4)+7(4-6)+9(6-1))=$\frac{1}{2}$×(-21-14+45)=5 unit.

So,  the total area of the three triangles=13.5 square units