Find the area of the composite figure. Make sure to show all steps and work for full credit.
6cm (the top base). 5 cm (the side, to the left). 14 cm (the bottom base).
Area of a triangle: 1/2 times b times h
Area of a parallelogram: base times height
First, find the area of the triangle on top:
1/2 (6 cm) * 5 cm = 15 cm²
Now, find the area of the parallelogram on the bottom:
14 cm * 5 cm = 70 cm²
Add the two areas together to find the total area of the composite figure:
15 cm² + 70 cm² = 85 cm²
Therefore, the area of the composite figure is 85 cm².
no the measurements are for the parallelogram, the triangle is sectioned off to the right it has to measurements. It' a scalene triangle
Apologies for the confusion.
Let's first find the area of the parallelogram at the bottom:
Area of a parallelogram = base x height
Area = 14 cm x 5 cm = 70 cm²
Now, let's find the area of the scalene triangle on the top right. Since it is a scalene triangle, we need to use Heron's formula to find the area.
First, calculate the semi-perimeter:
s = (6 cm + 14 cm + 5 cm) / 2 = 25 cm
Now, use Heron's formula to find the area of the triangle:
Area = √[s(s - 6)(s - 14)(s - 5)]
Area = √[25(25 - 6)(25 - 14)(25 - 5)]
Area = √[25(19)(11)(20)]
Area = √(104500)
Area ≈ 323.11 cm²
Finally, add the areas of the parallelogram and the triangle to get the total area of the composite figure:
Total Area = 70 cm² (parallelogram) + 323.11 cm² (triangle)
Total Area ≈ 393.11 cm²
Therefore, the area of the composite figure is approximately 393.11 cm².