Calculate the total area of the composite shapes. Shape 1: Square (side 20cm) and Triangle (base 20cm, height…

Question

Calculate the total area of the composite shapes. Shape 1: Square (side 20cm) and Triangle (base 20cm, height 20cm). Shape 2: Square (side 18cm) and Triangle (base 18cm, height 18cm).

ScanSolve AI Tutor · Accepted Answer

Here are the total areas for each shape:

1)

Identify the components of the shape.
The shape consists of a square and a right-angled triangle.
The square has sides of 20 cm.
The triangle has a base of 20 cm and a height of 20 cm.
Calculate the area of the square.
$\text{Area}_{\text{square}} = \text{side} \times \text{side} = 20 \text{ cm} \times 20 \text{ cm} = 400 \text{ cm}^2$
Calculate the area of the triangle.
$\text{Area}_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 20 \text{ cm} \times 20 \text{ cm} = 200 \text{ cm}^2$
Calculate the total area.
$\text{Total Area}_1 = \text{Area}_{\text{square}} + \text{Area}_{\text{triangle}} = 400 \text{ cm}^2 + 200 \text{ cm}^2 = \boxed{\text{600 cm}^2}$
2)
Identify the components of the shape.
The shape consists of a square and a right-angled triangle.
The square has sides of 18 cm.
The triangle has a base of 18 cm and a height of 18 cm.
Calculate the area of the square.
$\text{Area}_{\text{square}} = \text{side} \times \text{side} = 18 \text{ cm} \times 18 \text{ cm} = 324 \text{ cm}^2$
Calculate the area of the triangle.
$\text{Area}_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 18 \text{ cm} \times 18 \text{ cm} = 162 \text{ cm}^2$
Calculate the total area.
$\text{Total Area}_2 = \text{Area}_{\text{square}} + \text{Area}_{\text{triangle}} = 324 \text{ cm}^2 + 162 \text{ cm}^2 = \boxed{\text{486 cm}^2}$
3)
Identify the components of the shape.
The shape consists of a square and a right-angled triangle.
The square has sides of 24 cm.
The triangle has a base of 24 cm and a height of 24 cm.
Calculate the area of the square.
$\text{Area}_{\text{square}} = \text{side} \times \text{side} = 24 \text{ cm} \times 24 \text{ cm} = 576 \text{ cm}^2$
Calculate the area of the triangle.
$\text{Area}_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 24 \text{ cm} \times 24 \text{ cm} = 288 \text{ cm}^2$
Calculate the total area.
$\text{Total Area}_3 = \text{Area}_{\text{square}} + \text{Area}_{\text{triangle}} = 576 \text{ cm}^2 + 288 \text{ cm}^2 = \boxed{\text{864 cm}^2}$
4)
Identify the components of the shape.
The shape consists of a square and a right-angled triangle.
The square has sides of 32 cm.
The triangle has a base of 32 cm and a height of 32 cm.
Calculate the area of the square.
$\text{Area}_{\text{square}} = \text{side} \times \text{side} = 32 \text{ cm} \times 32 \text{ cm} = 1024 \text{ cm}^2$
Calculate the area of the triangle.
$\text{Area}_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 32 \text{ cm} \times 32 \text{ cm} = 512 \text{ cm}^2$
Calculate the total area.
$\text{Total Area}_4 = \text{Area}_{\text{square}} + \text{Area}_{\text{triangle}} = 1024 \text{ cm}^2 + 512 \text{ cm}^2 = \boxed{\text{1536 cm}^2}$

Calculate the total area of the composite shapes. Shape 1: Square (side 20cm) and Triangle (base 20cm, height 20cm). Shape 2: Square (side 18cm) and Triangle (base 18cm, height 18cm).

Step-by-step solution

Identify the components of the shape.

Calculate the area of the square.

Calculate the area of the triangle.

Calculate the total area.

Identify the components of the shape.

Calculate the area of the square.

Calculate the area of the triangle.

Calculate the total area.

Identify the components of the shape.

Calculate the area of the square.

Calculate the area of the triangle.

Calculate the total area.

Identify the components of the shape.

Calculate the area of the square.

Calculate the area of the triangle.

Calculate the total area.

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