Here are the step-by-step solutions for each triangle on the worksheet.
Triangle 1
*
Area: The formula is $\frac{1}{2} \times \text{base} \times \text{height}$.
* Base = $12\text{ ft}$, Height = $6\text{ ft}$.
* Calculation: $0.5 \times 12 \times 6 = 36$.
* Area =
$36\text{ sq ft}$
*
Perimeter: Add all three sides together ($4 + 8 + 12$).
* Perimeter =
$24\text{ ft}$
Triangle 2
*
Area: Base = $25\text{ ft}$, Height = $12\text{ ft}$.
* Calculation: $0.5 \times 25 \times 12 = 150$.
* Area =
$150\text{ sq ft}$
*
Perimeter: Add all three sides ($15 + 20 + 25$).
* Perimeter =
$60\text{ ft}$
Triangle 3
*
Area: Base = $6\text{ m}$, Height = $8\text{ m}$.
* Calculation: $0.5 \times 6 \times 8 = 24$.
* Area =
$24\text{ sq m}$
*
Perimeter: Add all three sides ($10 + 10 + 6$).
* Perimeter =
$26\text{ m}$
Triangle 4
*
Area: Look for the right angle symbol to find the base and height. Here, the base is $12\text{ cm}$ and the vertical height is $5\text{ cm}$. (The $6\text{ cm}$ and $8\text{ cm}$ lines are extra information not needed for the area of the whole triangle).
* Calculation: $0.5 \times 12 \times 5 = 30$.
* Area =
$30\text{ sq cm}$
*
Perimeter: Add the outer boundary lengths ($12 + 5 + 8$).
* Perimeter =
$25\text{ cm}$
Triangle 5
*
Area: This triangle is rotated. The base is $6\text{ cm}$ and the height (the line perpendicular to it) is $7\text{ cm}$.
* Calculation: $0.5 \times 6 \times 7 = 21$.
* Area =
$21\text{ sq cm}$
*
Perimeter: Add the three outer sides ($3 + 3 + 6$).
* Perimeter =
$12\text{ cm}$
Triangle 6
*
Area: This is a right-angled triangle. The legs act as the base and height. Base = $12\text{ m}$, Height = $16\text{ m}$.
* Calculation: $0.5 \times 12 \times 16 = 96$.
* Area =
$96\text{ sq m}$
*
Perimeter: Add all three sides ($16 + 12 + 18$).
* Perimeter =
$46\text{ m}$
Triangle 7
*
Area: Base = $2.2\text{ yd}$, Height = $2.5\text{ yd}$.
* Calculation: $0.5 \times 2.2 \times 2.5 = 2.75$.
* Area =
$2.75\text{ sq yd}$
*
Perimeter: Add the outer sides ($1.5 + 3.3 + 2.2$).
* Perimeter =
$7\text{ yd}$
Triangle 8
*
Area: Right-angled triangle. Base = $8\text{ yd}$, Height = $6\text{ yd}$.
* Calculation: $0.5 \times 8 \times 6 = 24$.
* Area =
$24\text{ sq yd}$
*
Perimeter: Add all three sides ($10 + 6 + 8$).
* Perimeter =
$24\text{ yd}$
──────────────────────────────────────
Final Answer:
1) Area = $36\text{ ft}^2$, Perimeter = $24\text{ ft}$
2) Area = $150\text{ ft}^2$, Perimeter = $60\text{ ft}$
3) Area = $24\text{ m}^2$, Perimeter = $26\text{ m}$
4) Area = $30\text{ cm}^2$, Perimeter = $25\text{ cm}$
5) Area = $21\text{ cm}^2$, Perimeter = $12\text{ cm}$
6) Area = $96\text{ m}^2$, Perimeter = $46\text{ m}$
7) Area = $2.75\text{ yd}^2$, Perimeter = $7\text{ yd}$
8) Area = $24\text{ yd}^2$, Perimeter = $24\text{ yd}$
Parent Tip: Review the logic above to help your child master the concept of area and perimeter triangle worksheet.
