Question

Can you find the lengths and areas, use the box on the right to help you find the correct answer.

Answer 1

Let's find the lengths and areas of the given figures.

• Question 1

Area of a:

Figure a has the shape of a square.

To find the area, let's find the side length, which is the hypotenuse of triangle b.

Apply Pythagorean Theorem:

`c^2=a^2+b^2`

Where:

`\begin{gathered} a=\sqrt[]{9}=3m \\ b=\sqrt[]{16}=4m \end{gathered}`

Thus, we have:

`\begin{gathered} c^2=a^2+b^2 \\ \\ c^2=3^2+4^2 \\ \\ c^2=9+16 \\ \\ c^2=25 \\ \\ \text{Take the square root of both sides:} \\ \sqrt[]{c^2}=\sqrt[]{25} \\ \\ c=5 \end{gathered}`

The side length of a is = 5 m

Therefore, to find the area of a, apply the formula for area of a square:

`\begin{gathered} A=l^2 \\ \\ A=5^2 \\ \\ A=25m^2 \end{gathered}`

Therefore, the area of a is 25 square meters

• Question 2

Length of b

b is the hypotenuse of the triangle, which is also the side length of figure a.

Therefore, the length of b is 5 m

• Question 3.

Length of C

To find the length of c, apply Pythagorean Theorem:

`144=81+c^2`

Let's solve for c from the equation:

Subtract 81 from both sides:

`\begin{gathered} 144-81=81-81+c^2 \\ \\ 63=c^2 \\ \\ \text{Take the square root of both sides:} \\ \sqrt[]{63}=\sqrt[]{c^2}^{} \\ \\ 7.94=c \\ \\ c=7.94 \end{gathered}`

Therefore, the length of c is 7.94 m

Question 4:

Area of d.

Figure d is a traingle.

To find the area, apply the formula:

`A=(1)/(2)bh`

Where:

Base, b = length of c = 7.94

Height, h = √81 = 9 m

Thus, we have:

`\begin{gathered} A=(1)/(2)\ast7.94\ast9 \\ \\ A=3.97\ast9 \\ \\ A=35.75m^2 \end{gathered}`

Therefore, the area of b is 35.73 square meters.

ANSWER:

1. H) 25

2. I) 5

3. A) 7.94

4. B.) 35.73