Find the total area of the composite figure below, composed of a triangle, a rectangle, and a square.

Question

ScanSolve AI Tutor · Accepted Answer

Let's find the total area of the composite figure.

Solution

The figure is composed of three shapes: a triangle (A), a rectangle (B), and a square (C).

1. Area of Shape A (Triangle)
The formula for the area of a triangle is $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ .

Identify the base and height of triangle A.
Base $= 6 \text{ cm}$
Height $= 8 \text{ cm}$
Substitute the values into the formula.
$\text{Area of A} = \frac{1}{2} \times 6 \text{ cm} \times 8 \text{ cm}$ $\text{Area of A} = \frac{1}{2} \times 48 \text{ cm}^2$ $\text{Area of A} = 24 \text{ cm}^2$
2. Area of Shape B (Rectangle)
The formula for the area of a rectangle is $\text{Area} = \text{length} \times \text{width}$ .
Identify the length and width of rectangle B.
Length $= 12 \text{ cm}$
Width $= 8 \text{ cm}$
Substitute the values into the formula.
$\text{Area of B} = 12 \text{ cm} \times 8 \text{ cm}$ $\text{Area of B} = 96 \text{ cm}^2$
3. Area of Shape C (Square)
The figure shows one side of C as $5 \text{ cm}$ . Since it's a square, both sides are $5 \text{ cm}$ . The formula for the area of a square is $\text{Area} = \text{side} \times \text{side}$ .
Identify the side length of square C.
Side $= 5 \text{ cm}$
Substitute the value into the formula.
$\text{Area of C} = 5 \text{ cm} \times 5 \text{ cm}$ $\text{Area of C} = 25 \text{ cm}^2$
4. Total Area
To find the total area, sum the areas of shapes A, B, and C.
Add the calculated areas.
$\text{Total Area} = \text{Area of A} + \text{Area of B} + \text{Area of C}$ $\text{Total Area} = 24 \text{ cm}^2 + 96 \text{ cm}^2 + 25 \text{ cm}^2$ $\text{Total Area} = \boxed{145 \text{ cm}^2}$

Answer