Question

2√5 times √8 plus 2√5 times √2 divide by 2. Any surds in the answer in their simplest form.

Answer 1

The area of the compound shape is 5√10 cm²

Explanation:

In the given shape, there is a rectangle and a right angle triangle.

i.e.,

Compund shape = Rectangle + Triangle

So,

Area of Compound Shape = Area of Rectangle + Area of Right Angle Triangle

For Rectangle;

• Length (l) = 2√5 cm
• Width (w) = √8cm = 2√2 cm

Formula;

• A = l × w

A = 2√5 × 2√2 cm

A = 4√10 cm²

For Triangle;

• Base (b) = 2 cm
• Height (h) = 2√5 cm

Formula;

• A = ½ × base × height

A = ½ × √2 × 2√5 cm

A = 1 × √2 × √5 cm

A = √10 cm²

Now,

Area of Compound Shape = Area of Rectangle + Area of Right Angle Triangle

A = 4√10 cm² + √10 cm²

A = 5√10 cm²

Thus, The area of the compound shape is 5√10 cm²