Answer: A = 33 in²
Step-by-step explanation:
<u>Given information:</u>
Longer side = 7 in
Shorter side = 4 in
Shorter Hypotenuse = 5 in
<u>Given formula:</u>
A = (1/2) × (d₁) × (d₂)
- A = area
- d₁ = The longer line (horizontal)
- d₂ = The shorter line (vertical)
Please refer to the attachment below for a graphical understanding
<u>Determine the length of the shorter side (vertical) through the Pythagorean theorem</u>
a² + b² = c² <em>(Pythagorean theorem)</em>
(4)² + b² = (5)² <em>(Substitute values into the equation)</em>
16 + b² = 25
b² = 25 - 16
b² = 9
b = 3 or b = -3 (rej)
<u>Substitute values into the given formula</u>
A = (1/2) × d₁ × d₂
A = (1/2) × (7 + 4) × (3 + 3)
<u>Simplify values in the parenthesis</u>
A = (1/2) × 11 × 6
<u>Simplify by multiplication</u>
A = (11/2) × 6

Hope this helps!! :)
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