Question

Find the area of the composite figure.
First, find the area of the triangle.
Triangle
bh
Area = [?] in.² 2
Rectangle
Area = [] in.²
4 in.
6 in.
Total Area of
Composite Figure = [ ] in.²
12 in.
12 in.

Answer 1

Answer:

$A_{\textsf{triangle}} = 24 \, \textsf{in}^2$

$A_{\textsf{rectangle}} = 72 \, \textsf{in}^2$

$\textsf{Total Area} = 96 \, \textsf{in}^2$

Step-by-step explanation:

To find the area of the composite figure, we first need to find the area of each individual component and then sum them up.

Area of the Triangle:

Given:

• Base of the triangle $= 12 \, \textsf{in}$
• Height of the triangle $= 4 \, \textsf{in}$

The area $A$ of a triangle is given by the formula:

$A_{\textsf{triangle}} = \dfrac{1}{2} \times \textsf{Base} \times \textsf{Height}$

$A_{\textsf{triangle}} = \dfrac{1}{2} \times 12 \times 4$

$A_{\textsf{triangle}} = 24 \, \textsf{in}^2$

Area of the Rectangle:

Given:

• Length of the rectangle $= 12 \, \textsf{in}$
• Width of the rectangle $= 6 \, \textsf{in}$

The area $A$ of a rectangle is given by the formula:

$A_{\textsf{rectangle}} = \textsf{Length} \times \textsf{Width}$

$A_{\textsf{rectangle}} = 12 \times 6$

$A_{\textsf{rectangle}} = 72 \, \textsf{in}^2$

Now, to find the total area of the composite figure, we add the areas of the triangle and the rectangle:

$\textsf{Total Area} = A_{\textsf{triangle}} + A_{\textsf{rectangle}}$

$\textsf{Total Area} = 24 + 72$

$\textsf{Total Area} = 96 \, \textsf{in}^2$

So, the total area of the composite figure is $96 \, \textsf{in}^2$.