Question

Find the area of the composite figure.
First, find the area of the parallelogram.
Parallelogram
Area = [?] cm²
Triangle
Area = [ ] cm²
12 cm
6 cm
Total Area of
Composite Figure = [ ] cm²
10 cm

Answer 1

Answer :

• area llgm = 72 cm^2
• area ∆ = 60 cm^2
• total area = 132 cm^2

Explanation :

area of a llgm is given by,

• area(p) = base x height
• area(p) = 12 cm x 6 cm
• area(p) = 72 cm^2

area of a triangle is given by,

• area(t) = 1/2 x base x height
• area(t) = 1/2 x 12 cm x 10 cm
• area(t) = 60 cm^2

total area of the figure is given by,

• area(f) = area(p) + area(t)
• area(f) = 72 cm^2 + 60 cm^2
• area(f) = 132 cm^2

Answer 2

Answer:

$A_{\textsf{parallelogram}} = 72 \, \textsf{cm}^2$

$A_{\textsf{triangle}} = 60 \, \textsf{cm}^2$

$\textsf{Total Area} = 132 \, \textsf{cm}^2$

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 Parallelogram:

Given:

• Base of the parallelogram $= 12 \, \textsf{cm}$
• Height of the parallelogram $= 6 \, \textsf{cm}$

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

$A_{\textsf{parallelogram}} = \textsf{Base} \times \textsf{Height}$

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

$A_{\textsf{parallelogram}} = 72 \, \textsf{cm}^2$

Area of the Triangle:

Given:

The opposite side of the parallelogram is equal. so

• Base of the triangle $= 12 \, \textsf{cm}$
• Height of the triangle $= 10 \, \textsf{cm}$

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

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

$A_{\textsf{triangle}} = \dfrac{1}{2} \times 12 \times 10$

$A_{\textsf{triangle}} = 60 \, \textsf{cm}^2$

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

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

$\textsf{Total Area} = 72 + 60$

$\textsf{Total Area} = 132 \, \textsf{cm}^2$

So, the total area of the composite figure is $132 \, \textsf{cm}^2$.