Question

7)a = 63.68 cm b = 81.56 cmc = 84 cm h = 60 cmarea: _____________perimeter: ___________type: ___________8)s = 50 mmh = 43.3 mmarea: ___________perimeter: ___________type: ___________9)s = 75 mmh = 65 mmarea: ___________perimeter: ___________type: _____________

Explanation:

Step1: Calculate area of triangle 7

Area formula: $\frac{1}{2} \times \text{base} \times \text{height}$
$\text{Area} = \frac{1}{2} \times 84 \times 50 = 2100 \, \text{cm}^2$

Step2: Calculate perimeter of triangle 7

Sum all side lengths: $a + b + c$
$\text{Perimeter} = 53.68 + 81.56 + 84 = 219.24 \, \text{cm}$

Step3: Identify type of triangle 7

All sides are different lengths, so it is a scalene triangle.

Step4: Calculate area of triangle 8

Area formula: $\frac{1}{2} \times \text{base} \times \text{height}$
$\text{Area} = \frac{1}{2} \times 50 \times 43.3 = 1082.5 \, \text{mm}^2$

Step5: Calculate perimeter of triangle 8

Sum all equal side lengths: $3 \times s$
$\text{Perimeter} = 3 \times 50 = 150 \, \text{mm}$

Step6: Identify type of triangle 8

All sides are equal, so it is an equilateral triangle.

Step7: Calculate area of triangle 9

Area formula: $\frac{1}{2} \times \text{base} \times \text{height}$
$\text{Area} = \frac{1}{2} \times 75 \times 65 = 2437.5 \, \text{mm}^2$

Step8: Calculate perimeter of triangle 9

Sum all equal side lengths: $3 \times s$
$\text{Perimeter} = 3 \times 75 = 225 \, \text{mm}$

Step9: Identify type of triangle 9

All sides are equal, so it is an equilateral triangle.

Answer:

Triangle 7:

Area: $2100 \, \text{cm}^2$
Perimeter: $219.24 \, \text{cm}$
Type: Scalene triangle

Triangle 8:

Area: $1082.5 \, \text{mm}^2$
Perimeter: $150 \, \text{mm}$
Type: Equilateral triangle

Triangle 9:

Area: $2437.5 \, \text{mm}^2$
Perimeter: $225 \, \text{mm}$
Type: Equilateral triangle